  Hawking radiation has thermal spectrum corresponding to the temperature
${T}_{H}={(8{\pi}M)}^{-1}$, where $M$ is the mass (energy) of the black hole.
Corrections to the Hawking radiation spectrum were discovered by Kraus and
Wilczek (1995) and Parikh and Wilczek (2000). Here I show that these
corrections follow directly from the basic principles of thermodynamics and
statistical mechanics. In essence, it is the Boltzmann factor that ought to be
corrected; corrections to the Hawking (or any other) radiation spectrum then
follow necessarily.
