When considering heat death, the important thing is not to consider the
temperature, but instead the
temperature gradient and differences in
potential energy.
As an ordered system (i.e., well-divided) flows towards chaos, the amount of work that can be extracted from such a system decreases. By the second law of thermodynamics, you cannot have any sort of release of energy without increasing the amount of chaos (entropy) in the system. Therefore, when the system is compeletly chaotic, that is, there is no gradient of potential energy within it, there will be no possibility of work being done within that system. Given that the Universe is a closed system, heat death is inevitable.
If it makes you feel better, just think that by the time heat death becomes a problem, humanity will be long dead, decomposed, and forgotten. OK, so maybe that doesn't make you feel any better.
Some people believe that black holes may be a way around this problem, but I can't give a good explanation why. I believe it has something to do with the fact that the gravity well of the singularity creates a nucleus that is hotter at it center than thermodynamics predicts.