  The problem of complete evaporation of Schwarzschild black holes raised by
Hawking is that one has an explosion of the temperature $T=1/8\pi M$ for
vanishing black hole mass M. We consider the Reissner-Nordstrom black hole and
note that if mass $M$ and charge Q<M satisfy the bound Q>M-C M^3, C>0 for small
M then the complete evaporation of black holes without blow-up of temperature
is possible. We describe curves on the surface of state equations such that the
motion along them provides complete evaporation. The radiation entropy follows
the Page curve and vanishes at the end of evaporation.
  Similar results for rotating Kerr, Schwarzschild-de-Sitter and
Reissner-Nordstrom-(Anti)-de-Sitter black holes are discussed.
