Roger Penrose's answer to that is that there is nothing to experience time, and with no time there is no way to measure speed and no concept of frequency and so no concept of distance. Without all that, the enormouse heat-death decayed universe still contains all the energy it ever did (because it can't be destroyed), and if there's no distance then the heat-death universe is identical to the pre-big-bang universe, and so there is no need for a big crunch and it can still be a cyclic thing where it explodes again, leaving the cosmic microwave background radiation as a remnant of the boundary between the previous aeon and the current one.
I like this response as with a true heat death of the universe nothing can move, so does time even exist at that point?
Alternately, heat death = where you fall asleep with the electric blanket on, wake up dehydrated and lacking all energy...