Time and entropy being fairly parallel concepts, Heat Death always amounts to an effective end of time since no meaningful action of any sort would be possible then, essentially the same as if time stopped. Or if you fell into a black hole, pretty much all Universe Death Theories of our life times involve an effective end of time, either from it halting from a crunch or this, or everything in time frozen black holes, or simply the turning into a lukewarm homogeneous thin vacuum where nothing meaningful can occur.