Temperature and entropy of a quantum black hole and conformal anomaly

Attention is paid to the fact that the temperature of a classical black hole can be derived from the extremality condition of its free energy with respect to the variation of the mass of a hole. For a quantum Schwarzschild black hole evaporating massless particles the same condition is shown to result in the one-loop temperature T= (8) ^-11+ (8M^2) ^-1 and entropy S=4M^2- expressed in terms of the effective mass M of a hole together with its radiation and the integral of the conformal anomaly that depends on the field species. Thus, in the given case quantum corrections to T and S turn out to be completely provided by the anomaly. When it is absent (=0), which happens in a number of supersymmetric models, the one-loop expressions of T and S preserve the classical form. On the other hand, if the anomaly is negative (0) an evaporating quantum hole seems to cease to heat up when its mass reaches the Planck scales.