Heat "death" is somewhat misleading. While we are no more after death, the universe exists without being alive and will still exist when it reaches heat death.
The way I learnt this as a student in a cosmology class, heat death means that there is only infrared radiation and matter in the form of the most stable element (iron in that lecture, nickel according to another reference), and on the way toward there, conditions will become too adverse for any lifeform to survive.
However, this class was taught before the apparent acceleration of the expansion of the universe was discovered, which should be a major game changer.
Another correction of what was mentioned in the thread: The energy will never be used up, it will just be distributed more evenly / the entropy will be much higher.