  When black holes are dynamical, event horizons are replaced by apparent and
trapping horizons. Conformal and Kerr-Schild transformations are widely used in
relation with dynamical black holes and we study the behaviour under such
transformations of quantities related to the thermodynamics of these horizons,
such as the Misner-Sharp-Hernandez mass (internal energy), the Kodama vector,
surface gravity, and temperature. The transformation properties are not those
expected on the basis of naive arguments.
