If the Universe is infinite, would heat death be impossible?
Heat death of the Universe doesn't mean that there is no energy in it, it means it has reached thermodynamic equilibrium and hence no useful energy in it. This could in theory occur in an infinite Universe.

Of course thermodynamics is statistical in nature, so an argument could be made that some extremely unlikely event in a region of the Universe could destroy thermal equilibrium in that region and that the larger the Universe the more likely that some region like that exists.