  A self-consistent approach to nonequilibrium radiation temperature is
introduced using the distribution of the energy over states. We begin
rigorously with ensembles of Hilbert spaces and end with practical examples
based mainly on the far from equilibrium radiation of lasers. We show that very
high, but not infinite, laser radiation temperatures depend on intensity and
frequency. Heuristic "temperatures" derived from a misapplication of
equilibrium arguments are shown to be incorrect. More general conditions for
the validity of nonequilibrium temperatures are also established.
