  The fate of black hole thermodynamics under Weyl transformations is
investigated by going back to the laws of black hole mechanics. It is shown
that the transformed surface gravity, that one would identify with the black
hole temperature in the conformal frame, as well as the black hole entropy,
that one would identify with the horizon area, cannot be invariant. It is also
shown that the conformally invariant surface gravity, attributed to the
so-called "conformal Killing horizon", cannot represent the black hole
temperature in the conformal frame. Finally, using familiar thought
experiments, we find that the effect a Weyl transformation should have on black
hole thermodynamics becomes even subtler than what is suggested by the laws of
black hole mechanics
