  The conventional Tolman temperature based on the assumption of the traceless
condition of energy-momentum tensor for matter fields is infinite at the
horizon if Hawking radiation is involved. However, we note that the temperature
associated with Hawking radiation is of relevance to the trace anomaly, which
means that the traceless condition should be released. So, a trace
anomaly-induced Stefan-Boltzmann law is newly derived by employing the first
law of thermodynamics and the property of the temperature independence of the
trace anomaly. Then, the Tolman temperature is quantum-mechanically generalized
according to the anomaly-induced Stefan-Boltzmann law. In an exactly soluble
model, we show that the Tolman factor does not appear in the generalized Tolman
temperature which is eventually finite everywhere, in particular, vanishing at
the horizon. It turns out that the equivalence principle survives at the
horizon with the help of the quantum principle, and some puzzles related to the
Tolman temperature are also resolved.
