Why must an infinite universe be infinitely hot?

Question

I think this was one of Shrodinger's thought experiments or supposed paradoxes. It might have been referred to as "Shrodinger's Oven".

I think my Fractal Foam Model of Universes has a solution, but I am ignorant of what the supposed problem is.

In case you're wondering, the solution is that there is an energy equivalent of space, so the expansion of space acts as an infinite heat sink.

Answer 1

It doesn't. Heat = Energy. Energy can't be created out of no where. Therefore, if the universe is infinite, at some point the molecules will be spread so far apart, that the heat will diminish from them almost completely.