I once heard of the hypothesis that once the last proton decays, the universe will once more be completely uniform in every way. With nothing to distinguish any part of the universe from any other part, space becomes meaningless and the universe has once more entered a state of nothingness much like how it was "before" the Big Bang.

So, in a sense, the heat death is not so different from the big bounce.

Unfortunately I did not bother to bookmark what I had read, and can no longer find a name or anything referring to it on the internet.