My understanding is that the Fermi temperature is a measure of the energy of a system at its lowest energy state. This suggests that at the Fermi temperature is a minimum temperature where the system can't radiate away any more energy. If this were a physical temperature it seems the system should radiate black body radiation. But then where would this energy come from? Rather than a physical temperature, would it be better to see this as a cutoff, like static friction, representing the cutoff where the lowest energy state is at thermal equilibrium with its surroundings, but above which excited states will be required?