I don't think space is the issue. Most people live 200 miles from the coast. If that gets as hot as the inland, people will fan out to find whatever shelter they can. While I hope there are cool materials science breakthroughs that can withstand high temperatures, I imagine a lot of people will make homes in caves and underground, like a nuclear bunker.
That would definitely change cultures and economies, but if you can't get out of those places, it might be your only option.
That would definitely change cultures and economies, but if you can't get out of those places, it might be your only option.