As the case with a lot of questions here, you are not focussing on world building here but rather trying to figure out what would happen to Earthly creatures when the sun gets in red giant phase.
There are times when evolution drives extremely fast. One of those times was the early part of Cambrian Period. This fast phase of evolution is known as Cambrian Explosion. Even then it took several millions of years for creatures to be distinctly different from their predecessors.
So strictly genetically speaking, a couple of hundred years is far far too less for any large scale evolutionary change to occur. You would at least require some tens of millions of years. And then too, I personally don't think any creature would be hardy enough to stay alive, considering that there would be no oceans on Earth at all, and no atmosphere either. Even extremophiles would go extinct because they would be simply boiled to death. Notice that while some hardy microbes can stay alive at very high temperatures, they do so only in aquatic environment. No bacteria can stay alive at 300 °C in dry conditions. That is the temperature of coal fire.
That's what Earth would be, then.