A Temperature Ceiling for Evaporating Primordial Black Holes from the Density Bound

As a black hole evaporates, it grows hotter. The Hawking temperature rises in inverse proportion to the remaining mass, so the final stages of evaporation are, in the semiclassical treatment, a runaway towards arbitrarily high temperatures reached at arbitrarily small masses. The headline computed values are: M min g = 1.000e+13; T max K = 1.227e+13; T max MeV = 1.057e+03; T Pl K = 1.417e+32. This is a simulated and computed study, not a measurement; the code and outputs are deposited alongside the text.