You clearly don't understand the process of evolution. What causes problems for the species living on Earth at any one time isn't hot, or cold - it's the sudden shift from (predominantly) one to (predominantly) the other.
Sure, "life" will bounce back. But only if you look at it at the coarsest level. Because evolution doesn't work via individuals or individual species adapting - it works by preferentially killing off those that aren't already (by sheet, random luck of genetics) able to handle the current environment, while those that survive repopulate to fill the gap.
Every species alive on earth today is the product of hundreds to tens of thousands of generations in a climate not that far dissimilar to what we have now - and before that, the change from previous climates was gradual, over the course of tens to hundreds of generations. Even so, the change from the ice ages to modern conditions put an end to many previously successful species.
This time around, we're inducing a similar-scale change in the space of a few generations. The result won't be pretty.
