Hawking ("A Briefer History of Time") speaks of a "hot infinite universe at the time of the Big Bang. But w hen the universe would have started infinitely hot, despite cooling then it would still infinitely hot. That would be then, as in the figures. There are infinitely many natural numbers: 1, 2, 3, etc. If you like a particular Number of takes away, for example, one hundred million pieces, then remain still remain infinitely many natural numbers. So it is with infinity. Or Hawking (or his translator) uses this term and flippant means by "infinitely hot" just "very very hot," for example, 500 billion degrees. Quite possible that it was even hotter at the beginning ( here is 32 degrees from 10 to the speech), but not infinitely hot. Otherwise it would forever for anything to get too hot.
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