Xjyuk

Humans are the equivalent of bacteria to planet-eating monsters. And since, as we all know, eating humans is dangerous business, these monsters have decided to cook our great planet Earth before eating it.

Handwaving the monsters and all that comes with them, what is the minimum temperature they have to heat up the Earth to before eating it in order to eliminate humans and prevent possible infections?

Luckily for us, their ovens are slow and the Earth heats up slowly (around 30°F per year), which, I assume, would give use enough time to react to the change in temperature and allow us to start building infrastructure to prevent our inevitable death. Though, of course, once we're in the oven there's no leaving it.

Everything except for the monsters and the fact the Earth is heating up at an alarming rate, is the same as it is today.

I'm assuming there is no way to survive past the boiling point, though maybe there are ways to handle it if we keep water at higher pressure, but I also think we'd be able to withstand more than 160°F which would normally be deadly pretty quickly to a single human.

Unshielded humans will expire above 40 C

Well-prepared humans should be able to hang on to 1000 C and more for some time.

Due to our temperature management, humans can withstand temperatures above 100C for hours, and between 40 and 50C for days. However, all natural temperature management depends on evaporation and works only in low humidity. In high humidity, human won't be able to cool below the ambient level, so body temperature just above 40C would be fatal. If entire Earth is in the oven, it would become an equivalent of runaway greenhouse effect, and all surface would become uniformly hot and humid.

But if we can build a cooling enclosure with independent power source, humans can hold on at much higher temperatures. The key here is to provide effective thermal insulation and cooling. We currently don't have refrigeration units capable of working at very high temperatures, but below 1000C the challenge would be engineering one, not scientific. Above 1000C the difficulties would multiply and it is difficult to tell whether durable shelter can be constructed. And I guess at 2000 C the answer is "no" - we can not build it with today's tech level.

The humans are toast (well, medium rare anyway).

Short version : ten degrees Celsius should do it, twenty would be more than enough.

Luckily for us, their ovens are really slow and the Earth heats up really slowly (a few degrees celcius every year) Which, I assume would give use enough time to react to the change in temperature and allow us to start building infrastructure to prevent our inevitable death. Though, of course, once we're in the oven there's no leaving it.

Have a quick look at the news. Scientists have been patiently (and impatiently) explaining to everyone that we're screwing up the planet's weather and, hey, we call it global warming and it's going to be bad.

And in the many years since they started doing this precisely how much action has been taken by the powers that be to do anything constructive about this : nothing.

So the assumption humanity as a whole, which has never acted entirely together on a single project and is the universe's prime example of "cut of your nose to spite your face", will act in a mere five years to do something is the wildest optimism.

That said ...

Everything except for the monsters and the fact the Earth is heating up at an alarming rate, is the same as it is today.

Exactly the same as it is, because we're already heating up the atmosphere at an alarming rate ourselves. :-(

Well we don't function for extended periods at high temperatures and high humidity. The Mayo Clinic has a page on Heat Exhaustion and it's worth reading. In short at normal humidity levels you can just about cope with $37^circ C$, but as humidity rises you'll start really over-heating at "only" $33^circ C$.

Well in your scenario humidity will rise almost everywhere (hard to be precise), and that means much hotter feeling and much more difficulty doing basic tasks. As your temperature rise is about a few degrees every year, it's only gong to take a year to make some places barely livable and a mere three years to make even places like Ireland become a weltering tropical hell.

But that's OK as the ice cap will rapidly disintegrate in those temperature rises and the massive worldwide flooding, torrential rainfall and resulting landslides and other issues will render most of the inhabitable areas real disaster zones.

On this time scale ( a few years, not even five ) they won't even have set up committees to argue about whose fault it is nothing is being done, let alone solve the problem. In practical terms there is no way the world's industrial and food production systems will survive with such enormous damage and I'd expect worldwide famine and a reduction in industrial and economic output that would be catastrophic and make it virtually impossible to develop a response to the crisis (even if it was politically possible).

Note that all life on the planet will be affected, from ocean plankton to penguins. Nothing currently living on Earth (with a few oddball exceptions) is capable of adapting that quickly to both a huge climate change (that's increases in pace) and the sudden destruction of the ecosystems they depend on. We depend on all that other life to keep us going, so our survival alone is not an option.

If the aliens keep pouring on the heat and increasing temperature at that rate, it's impossible for a sustained survival of more than some thousands of humans in e.g. a specially built emergency bunkers. But even these can't survive indefinitely. After ten years or so (imagine trying to store and grow food in such a system) the food will start to run out, and the power systems will fail as will heat regulation (because the outside keep getting hotter). There won't be infrastructure to supply parts to replace failing equipment. Things will rapidly go downhill as that happens and in say twenty years even these shelters would be lifeless.

By twenty years or so, while the temperature is notionally going to increase by some $60^circ C$ (which is essentially instant death), the atmosphere will most likely have tipped into runaway greenhouse effect and we'll be heading towards (if not actually in) an atmosphere more like Venus than anything you'd find on Earth now.

Once again, WB SE has killed the glorified monkeys. Yay. :-)

Cell death occurs at 65 degrees Celcius or 149 F. I am informed that is pretty much universal for cellular organisms on our planet, or at least not those living on undersea vents or boiling mud. As noted in a previous answer, human beings are adept at creating temperature controlled enclosures and depending on available power some could survive indefinitely.

This temperature will also kill the plants and bacteria on the planet -- assuming they had a way to raise the temperature equally given we have large bodies of water that will constrain local temperatures to 100 degrees Celcius until they boil away.

It seems odd that humans are lethal pathogens to planet eaters, and not goats, cattle, leaves. Unless it is our intelligence and tenacious drive to survive that makes us dangerous. SO, maybe consider alien phages that swarm the planet-devouring those pesky virulent pathogens. Sort of like the planet-eaters immune system cleanses the planet before it eats it.

No temperature is feasible.

This is because by the time the Earth becomes fully uninhabitable at the rate of heating stated by the OP, humans could build rockets to escape the Earth and colonize the other stellar bodies in the Solar system. This would potentially include the planet-eating monsters, and it might include any other stellar bodies that the planet-eaters have decided not to eat (e.g. possibly including asteroids or comets).

Potentially quite large rockets, too, since it's entirely possible that the Nuclear Test Ban Treaty will be torn up to facilitate the development of Orion Drive-style nuclear pulse rockets, which could carry 6000 tons to the moon and back on one tank of fuel using 1960s technology.

Additionally, while the temperature outside might rapidly become uninhabitable, it's entirely possible for humanity to build large climate-controlled structures to live in while this construction work is underway, along with hostile environment suits to let them walk around in temperatures that would otherwise kill them.