  It is shown that the surface gravity and temperature of a stationary black
hole are invariant under conformal transformations of the metric that are the
identity at infinity. More precisely, we find a conformal invariant definition
of the surface gravity of a conformal Killing horizon that agrees with the
usual definition(s) for a true Killing horizon and is proportional to the
temperature as defined by Hawking radiation. This result is reconciled with the
intimate relation between the trace anomaly and the Hawking effect, despite the
{\it non}invariance of the trace anomaly under conformal transformations.
