A post–Heat Death universe is, essentially, a very large, very slightly warmed box, with statistical mechanics stepping in to provide the random fluctuations. If the Big Bang is a state the universe has been in once, and the post–Heat Death universe is eternal (so eternal that, having lost the arrow of time, past and future are meaningless), there’s no reason a Big Bang can’t fluctuate out of the vacuum to start the universe anew.
