As defined by Wikipedia:
The heat death of the universe is a suggested ultimate fate of the universe in which the universe has diminished to a state of no thermodynamic free energy and therefore can no longer sustain processes that consume energy (including computation and life). Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work.
Does it even make sense to describe temperature in the system described? If so, would it be a very cold system or a very hot system?