I have just learned about the pretty cool idea about negative temperature (although it is "hotter" then positive temperature...) of a two level system. The condition for having negative temperature is the energy of the system has to have upper bound. It left me wondering :

If the observation of positive temperature ~2K of microwave background radiation suggests that our universe' total energy is unbounded? Are they anyway possibly linked? How do we measure negative temperature (if it were the case)?