How could life evolve when exposed to high temperature?

Edit: In the scenario that the temperature of a given area increases constantly over 30 million years (slowly enough for species to adapt) starting at 20°C and ending at 90°C, what are the possible species' evolutions in order to survive?

This question has a very large scope so here are some presicion.

Why an area?

I'm talking about area and not about an entire world in order to ignore any heavy climatic modification that would cause very abrupt change. For example, pole melting that would cause a flood.

Which species?

Well, I'm interested in plants, animals as well as humans but I'm not interested in technological evolution, only biological.

Which temperature are we talking about?

Well, I don't have any precise temperature, but I'd like temperatures higher that what we usually find on Earth. This means starting at 40°C and rising until life is no longer possible. One limit of temperature for life (as we know it) is water's boiling temperature (usually around 100°C). But water's boiling point depends on pressure. If pressure goes up, so will the boiling point.

Edit: Let's assume that the final temperature achieved is 90°C.

Edit: What is the time frame? I don't really know what timescale to use, but since you want it let's use human evolution timescale. Based on Wikipedia, the first Hominidae appeared 28 millions years ago. So let's say that our temperature increase slowly and constantly during 30 million years.

Also, my question concerns a global elevation of temperatures at all time (day and night) and at the surface.

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On Earth, the highest tempeature are usually achieved in arid or desertic areas. During the day, temperature can go up to 50°C or more but during the night, temperatures drop significantly. That's why wildlife is nowhere to be seen during day and very active during night. This huge gap between day and night temperature made desertic wild life not a good example to answer my question.

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If you want some precision that I've not given, feel free to comment.