Both the "heat" and "death" part of heat death are a bit of a misnomer: it's not so much about things being so cold as to be dead, and it's definitely not about

Both the "heat" and "death" part of heat death are a bit of a misnomer: it's not so much about things being so cold as to be dead, and it's definitely not about being spread out so much no interactions happen anymore: it's purely about the universe being in state of thermodynamic equilibrium, where interactions can still happen but do not increase entropy. In theory, the entire universe could be a million kelvin plasma, but once it reaches universal thermodynamic equilibrium, that's its "heat death".