We are adaptable creatures with command of technology. So we’ve got that going for us. We also have temperature limitations in which we can live, and so do our food sources. Then there’s the issue of potable water.

It really depends on how far we’re pushed the planet’s ecosphere. It could do like before (most recent is the PETM) and hover high, then eventually equalize back into something not the same as we had, but similar. It’s done this before, albeit after millions of years. Or it could find a new equilibrium in another state, aka hothouse. Not Venus-like, as some media has spun it, but its own version of feedback to retain a lot more heat than now. Not great for anything that evolved in this climate.

Fun fact: the PETM was the most recent heating event, 56 million years ago. Some species went extinct, others were able to adapt and survive as they evolved into smaller forms. The fun fact is that they adapted because the rate of heating change was over a large amount of time, many hundreds of thousands of years. Now look at us, a spike on the geological temperature graph in (looks at data) less than a 100 years (a few decades, really). So what kind of inertia does a more rapid acceleration usually give compared to a slower one? But hothouse Earth is just a speculation, just a guess. We don’t know how far this will go.

But will that subsequent civilization get to space again?

Isolated pockets in relatively protected areas. Global society won’t survive it. Most of the places we grow food won’t be able to grow food, that’s already accelerating. Ocean acidification kills that food source. Blue ocean event accelerates runaway heating leading to massive hurricane force continental storms. Amoc shuts down and Europe ices over. Humanity may persist but civilization won’t.