[jacknobody]

Ancient humans are thought by some researchers to have done much the same. The deep underground artworks in some French caves are said to be evidence of humans escaping the cold.

There's a reason I can think of that it might not work so well again. Lots of non-human animals survived the cold quite well, so there was game for those ancient ancestors to hunt, but there might be much less game surviving in great heat.

[RetroTechie]

And having game to hunt or not, is relevant to modern citizens how?

[jacknobody]

Post-apocalyptic citizens will get hungry too, although heat death isn't the usual apocalyptic scenario.