Yes, I know there are several topics about, but no one referred to my case. While colormap seems works only with plots, how can I draw a multicolor curve with smooth gradient? This is my attempt:

documentclassarticle
usepackage[T1]fontenc
usepackagelmodern
usepackagemakecell
setcellgapes5pt
usepackagebooktabs
usepackageamsmath,amssymb,amsfonts,systeme,mathtools 
usepackagepgfplots
usepackagefloat

begindocument

beginfigure[H]
centering
begintikzpicture
 beginaxis[
 ticks=none,
 grid=none,
 xmin=0,xmax=100,
 ymin=0,ymax=100,
 axis lines = middle,
 set layers,
 xlabel=$t$,ylabel=$T$,
 x label style=at=(1,0),right,
 y label style=at=(0,1),above,
 colormap=redbluergb255(0cm)=(255,0,0); rgb255(1cm)=(0,0,255)
 ]
 draw [ultra thick] (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
 node[inner sep=0pt, label=[outer sep=-2pt]45:A] at (20,90) ;
 node[label=[outer sep=-2pt]45:B] at (25,60) ;
 node[label=[outer sep=-2pt]45:C] at (35,45) ;
 node[label=[outer sep=-2pt]45:D] at (70,45) ;
 node[label=[outer sep=-2pt]45:E] at (90,20) ;
 addplot[only marks, mark options=solid,draw=green,fill=green]
 coordinates 
 (20,90) (25,60) (35,45) (70,45) (90,20)
 ;
 endaxis
endtikzpicture
endfigure

enddocument

Can you help me?

Thank you in advance

As you said, colormaps works with plots. In your code there is indeed a plot, but only for plotting the marks and hence not the line. This one is drawn with the draw command inside the axis. Therefore, you have to add a gradient color to your line.

Gradient with two colors

For instance, using the solution by Mark Wibrow to How to draw an arrow with two colors? you can add a color gradient using path and the defined shading path option in tikset. Then with left color=<color> and right color=<color> (or top color=<color> and bottom color=<color>) you have a gradient with only two colors.

Output:

Code:

documentclassarticle
usepackage[T1]fontenc
usepackagelmodern
usepackagemakecell
setcellgapes5pt
usepackagebooktabs
usepackageamsmath,amssymb,amsfonts,systeme,mathtools 
usepackagepgfplots
usepackagefloat
usetikzlibrarydecorations.markings,fadings

%https://tex.stackexchange.com/questions/137357/how-to-draw-an-arrow-with-two-colors
makeatletter
newififtikz@shading@path

tikzset
 % There are three circumstances in which the fading sep is needed:
 % 1. Arrows which do not update the bounding box (which is most of them).
 % 2. Line caps/joins and mitres that extend outside the natural bounding 
 % box of the path (these are not calculated by PGF).
 % 3. Other reasons that haven't been anticipated.
 fading xsep/.store in=pgfpathfadingxsep,
 fading ysep/.store in=pgfpathfadingysep,
 fading sep/.style=fading xsep=#1, fading ysep=#1,
 fading sep=0.0cm,
 shading path/.code=%
 % Prevent this stuff happning recursively.
 iftikz@shading@path%
 else%
 tikz@shading@pathtrue%
 % tikz@addmode installs the `modes' (e.g., fill, draw, shade) 
 % to be applied to the path. It isn't usualy for doing more
 % changes to the path's construction.
 tikz@addmode%
 pgfgetpathpgf@currentfadingpath%
 % Get the boudning box of the current path size including the fading sep
 pgfextract@processpgf@fadingpath@southwestpgfpointaddpgfqpointpgf@pathminxpgf@pathminy%
 pgfpoint-pgfpathfadingxsep-pgfpathfadingysep%%
 pgfextract@processpgf@fadingpath@northeastpgfpointaddpgfqpointpgf@pathmaxxpgf@pathmaxy%
 pgfpointpgfpathfadingxseppgfpathfadingysep%
 % Clear the path
 pgfsetpathpgfutil@empty% 
 % Interrupt the path and picture to create a fading.
 pgfinterruptpath%
 pgfinterruptpicture%
 begintikzfadingfrompicture[name=.]
 path [shade=none,fill=none, #1] pgfextra%
 % Set the softpath. Any transformations in #1 will have no effect.
 % This will *not* update the bounding box...
 pgfsetpathpgf@currentfadingpath%
 % ...so it is done manually.
 pgf@fadingpath@southwest
 expandafterpgf@protocolsizesthepgf@xthepgf@y%
 pgf@fadingpath@northeast%
 expandafterpgf@protocolsizesthepgf@xthepgf@y%
 ;
 % Now get the bounding of the picture.
 xdefpgf@fadingboundingbox@southwestnoexpandpgfqpointthepgf@picminxthepgf@picminy%
 xdefpgf@fadingboundingbox@northeastnoexpandpgfqpointthepgf@picmaxxthepgf@picmaxy%
 %
 endtikzfadingfrompicture%
 endpgfinterruptpicture%
 endpgfinterruptpath%
 % Install a rectangle that covers the shaded/faded path picture. 
 pgfpathrectanglecornerspgf@fadingboundingbox@southwestpgf@fadingboundingbox@northeast%
 % Make the fading happen.
 deftikz@path@fading.%
 tikz@mode@fade@pathtrue%
 tikz@fade@adjustfalse%10pt
 % Shift the fading to the mid point of the rectangle
 pgfpointscale0.5pgfpointaddpgf@fadingboundingbox@southwestpgf@fadingboundingbox@northeast%
 edeftikz@fade@transformshift=(thepgf@x,thepgf@y)%
 %
 fi%
 



begindocument

beginfigure[H]
centering
begintikzpicture
 beginaxis[
 ticks=none,
 grid=none,
 xmin=0,xmax=100,
 ymin=0,ymax=100,
 axis lines = middle,
 set layers,
 xlabel=$t$,ylabel=$T$,
 x label style=at=(1,0),right,
 y label style=at=(0,1),above,
 %colormap=redbluergb255(0cm)=(255,0,0); rgb255(1cm)=(0,0,255)
 ]
 path [left color=red, right color=blue, shading path=draw=transparent!0, ultra thick,]
 (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
% draw [ultra thick] (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
 node[inner sep=0pt, label=[outer sep=-2pt]45:A] at (20,90) ;
 node[label=[outer sep=-2pt]45:B] at (25,60) ;
 node[label=[outer sep=-2pt]45:C] at (35,45) ;
 node[label=[outer sep=-2pt]45:D] at (70,45) ;
 node[label=[outer sep=-2pt]45:E] at (90,20) ;
 addplot[only marks, mark options=solid,draw=green,fill=green]
 coordinates 
 (20,90) (25,60) (35,45) (70,45) (90,20)
 ;
 endaxis
endtikzpicture
endfigure

enddocument

Gradient with multicolors

For a multicolor gradient there is also a possibility. The aforementioned solution pass a gradient of two colors to the line color with the commands of the Shading library (Chapter 69, p.737). Therefore, if we are able to pass a multicolor gradient to Mark Wibrow´s solution, we have it done. Thankfully, Mark Wibrow gives us also the solution in the answer to How to draw gradient arrows with Tikz. Just combining both of them we can set a desired multicolor gradient.

Output with shading1:

Output with shading2:

Output with shading3:

Code:

documentclassarticle
usepackage[T1]fontenc
usepackagelmodern
usepackagemakecell
setcellgapes5pt
usepackagebooktabs
usepackageamsmath,amssymb,amsfonts,systeme,mathtools 
usepackagepgfplots
usepackagefloat
usetikzlibrarydecorations.markings,fadings

%https://tex.stackexchange.com/questions/137357/how-to-draw-an-arrow-with-two-colors
makeatletter
newififtikz@shading@path

tikzset
 % There are three circumstances in which the fading sep is needed:
 % 1. Arrows which do not update the bounding box (which is most of them).
 % 2. Line caps/joins and mitres that extend outside the natural bounding 
 % box of the path (these are not calculated by PGF).
 % 3. Other reasons that haven't been anticipated.
 fading xsep/.store in=pgfpathfadingxsep,
 fading ysep/.store in=pgfpathfadingysep,
 fading sep/.style=fading xsep=#1, fading ysep=#1,
 fading sep=0.0cm,
 shading path/.code=%
 % Prevent this stuff happning recursively.
 iftikz@shading@path%
 else%
 tikz@shading@pathtrue%
 % tikz@addmode installs the `modes' (e.g., fill, draw, shade) 
 % to be applied to the path. It isn't usualy for doing more
 % changes to the path's construction.
 tikz@addmode%
 pgfgetpathpgf@currentfadingpath%
 % Get the boudning box of the current path size including the fading sep
 pgfextract@processpgf@fadingpath@southwestpgfpointaddpgfqpointpgf@pathminxpgf@pathminy%
 pgfpoint-pgfpathfadingxsep-pgfpathfadingysep%%
 pgfextract@processpgf@fadingpath@northeastpgfpointaddpgfqpointpgf@pathmaxxpgf@pathmaxy%
 pgfpointpgfpathfadingxseppgfpathfadingysep%
 % Clear the path
 pgfsetpathpgfutil@empty% 
 % Interrupt the path and picture to create a fading.
 pgfinterruptpath%
 pgfinterruptpicture%
 begintikzfadingfrompicture[name=.]
 path [shade=none,fill=none, #1] pgfextra%
 % Set the softpath. Any transformations in #1 will have no effect.
 % This will *not* update the bounding box...
 pgfsetpathpgf@currentfadingpath%
 % ...so it is done manually.
 pgf@fadingpath@southwest
 expandafterpgf@protocolsizesthepgf@xthepgf@y%
 pgf@fadingpath@northeast%
 expandafterpgf@protocolsizesthepgf@xthepgf@y%
 ;
 % Now get the bounding of the picture.
 xdefpgf@fadingboundingbox@southwestnoexpandpgfqpointthepgf@picminxthepgf@picminy%
 xdefpgf@fadingboundingbox@northeastnoexpandpgfqpointthepgf@picmaxxthepgf@picmaxy%
 %
 endtikzfadingfrompicture%
 endpgfinterruptpicture%
 endpgfinterruptpath%
 % Install a rectangle that covers the shaded/faded path picture. 
 pgfpathrectanglecornerspgf@fadingboundingbox@southwestpgf@fadingboundingbox@northeast%
 % Make the fading happen.
 deftikz@path@fading.%
 tikz@mode@fade@pathtrue%
 tikz@fade@adjustfalse%10pt
 % Shift the fading to the mid point of the rectangle
 pgfpointscale0.5pgfpointaddpgf@fadingboundingbox@southwestpgf@fadingboundingbox@northeast%
 edeftikz@fade@transformshift=(thepgf@x,thepgf@y)%
 %
 fi%
 

makeatother
%-------------------------------------------------------------------------------------
%https://tex.stackexchange.com/questions/197793/how-to-draw-gradient-arrows-with-tikz
makeatletter
defcreateshadingfromlist#1#2#3%
 pgfutil@tempcnta=0relax
 pgfutil@forpgf@tmp:=#3doadvancepgfutil@tempcnta by1%
 ifnumpgfutil@tempcnta=1relax%
 edefpgf@speccolor(0)=(#3);color(100)=(#3)%
 else%
 pgfmathparse50/(pgfutil@tempcnta-1)letpgf@step=pgfmathresult%
 %
 pgfutil@tempcntb=1relax%
 pgfutil@forpgf@tmp:=#3do%
 ifnumpgfutil@tempcntb=1relax%
 edefpgf@speccolor(0)=(pgf@tmp);color(25)=(pgf@tmp)%
 else%
 ifnumpgfutil@tempcntb<pgfutil@tempcntarelax%
 pgfmathparse25+pgf@step/4+(pgfutil@tempcntb-1)*pgf@step%
 edefpgf@specpgf@spec;color(pgfmathresult)=(pgf@tmp)%
 else%
 edefpgf@specpgf@spec;color(75)=(pgf@tmp);color(100)=(pgf@tmp)%
 fi%
 fi%
 advancepgfutil@tempcntb by1relax%
 %
 fi%
 csname pgfdeclare#2shadingendcsname#1100pgf@spec%

makeatother

createshadingfromlistshading1verticalred,yellow,green,cyan,blue
createshadingfromlistshading2verticalred,green,yellow
createshadingfromlistshading3verticalred,black,blue,green,cyan,orange,yellow


begindocument

beginfigure[H]
centering
begintikzpicture
 beginaxis[
 ticks=none,
 grid=none,
 xmin=0,xmax=100,
 ymin=0,ymax=100,
 axis lines = middle,
 set layers,
 xlabel=$t$,ylabel=$T$,
 x label style=at=(1,0),right,
 y label style=at=(0,1),above,
% colormap=redbluergb255(0cm)=(255,0,0); rgb255(1cm)=(0,0,255)
 ]
 path [shading=shading1, shading path=draw=transparent!0, ultra thick,]
 (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
% draw [ultra thick] (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
 node[inner sep=0pt, label=[outer sep=-2pt]45:A] at (20,90) ;
 node[label=[outer sep=-2pt]45:B] at (25,60) ;
 node[label=[outer sep=-2pt]45:C] at (35,45) ;
 node[label=[outer sep=-2pt]45:D] at (70,45) ;
 node[label=[outer sep=-2pt]45:E] at (90,20) ;
 addplot[only marks, mark options=solid,draw=green,fill=green]
 coordinates 
 (20,90) (25,60) (35,45) (70,45) (90,20)
 ;
 endaxis
endtikzpicture
endfigure

enddocument

This is a slightly different approach than in Ñako's nice answer in that you can specify the color (and the line width) as a function of the fraction of the path. You may think of this as a version of point meta, in which you can specify the meta as a function of the decorated path length. This code is based on this answer as well as this answer. The first example uses a linear dependence on the path length fraction, and the second one an oscillating function, and also features a varying line width. Please note also that you can use point meta to achieve this (see e.g. this answer), but then you cannot use bend left and friends.

documentclassarticle
usepackage[T1]fontenc
usepackagelmodern
usepackagepgfplots
pgfplotssetcompat=1.16
usetikzlibrarydecorations
usepackagefloat
pgfkeys/pgf/decoration/.cd,
 start color/.store in=startcolor,
 start color=black,
 end color/.store in=endcolor,
 end color=black,
 varying line width steps/.initial=100

pgfdeclaredecorationwidth and color changeinitial
 stateinitial[width=0pt, next state=line, persistent precomputation=%
 pgfmathparsepgfdecoratedpathlength/pgfkeysvalueof/pgf/decoration/varying line width steps%
 letincrement=pgfmathresult%
 defx0%
 ]
 stateline[width=increment pt, persistent postcomputation=%
 pgfmathsetmacroxx+increment
 ,next state=line]%
 pgfmathparsevaryinglw(x/pgfdecoratedpathlength)
 pgfsetlinewidthpgfmathresult pt%
 pgfpathmovetopgfpointorigin%
 pgfmathsetmacrosteplength1.4*increment
 pgfpathlinetopgfqpointsteplength pt0pt%
 pgfmathsetmacroyvaryingcolor(100*(x/pgfdecoratedpathlength))
 pgfsetstrokecolorendcolor!y!startcolor%
 pgfusepathstroke%
 
 statefinal%
 pgfmathparsevaryinglw(1) 
 pgfsetlinewidthpgfmathresult pt%
 pgfpathmovetopgfpointorigin%
 pgfmathsetmacroyvaryingcolor(100*(x/pgfdecoratedpathlength))
 colorendcolor!y!startcolor%
 pgfusepathstroke% 
 

begindocument

beginfigure[H]
centering
begintikzpicture[declare function=varyinglw(x)=1;varyingcolor(x)=x;]
 beginaxis[
 ticks=none,
 grid=none,
 xmin=0,xmax=100,
 ymin=0,ymax=100,
 axis lines = middle,
 set layers,
 xlabel=$t$,ylabel=$T$,
 x label style=at=(1,0),right,
 y label style=at=(0,1),above,
 colormap=redbluergb255(0cm)=(255,0,0); rgb255(1cm)=(0,0,255)
 ]
 draw [decorate,decoration=width and color change,
 start color=red,end color=blue] (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
 node[inner sep=0pt, label=[outer sep=-2pt]45:A] at (20,90) ;
 node[label=[outer sep=-2pt]45:B] at (25,60) ;
 node[label=[outer sep=-2pt]45:C] at (35,45) ;
 node[label=[outer sep=-2pt]45:D] at (70,45) ;
 node[label=[outer sep=-2pt]45:E] at (90,20) ;
 addplot[only marks, mark options=solid,draw=green,fill=green]
 coordinates 
 (20,90) (25,60) (35,45) (70,45) (90,20)
 ;
 endaxis
endtikzpicture
endfigure

beginfigure[H]
centering
begintikzpicture[declare
function=varyinglw(x)=2+sin(360*x);varyingcolor(x)=50+50*sin(7.2*x);]
 beginaxis[
 ticks=none,
 grid=none,
 xmin=0,xmax=100,
 ymin=0,ymax=100,
 axis lines = middle,
 set layers,
 xlabel=$t$,ylabel=$T$,
 x label style=at=(1,0),right,
 y label style=at=(0,1),above,
 colormap=redbluergb255(0cm)=(255,0,0); rgb255(1cm)=(0,0,255)
 ]
 draw [decorate,decoration=width and color change,
 start color=red,end color=blue] (20,90) to[out=270,in=110] (25,60) to[out=335,in=115] (35,45) to[out=0,in=180] (70,45) to[out=305,in=150] (90,20);
 node[inner sep=0pt, label=[outer sep=-2pt]45:A] at (20,90) ;
 node[label=[outer sep=-2pt]45:B] at (25,60) ;
 node[label=[outer sep=-2pt]45:C] at (35,45) ;
 node[label=[outer sep=-2pt]45:D] at (70,45) ;
 node[label=[outer sep=-2pt]45:E] at (90,20) ;
 addplot[only marks, mark options=solid,draw=green,fill=green]
 coordinates 
 (20,90) (25,60) (35,45) (70,45) (90,20)
 ;
 endaxis
endtikzpicture
endfigure

enddocument