  Non-extremal black holes are endowed with geometric invariants related to
their horizon areas. We extend earlier work on hot attractor black holes to
higher dimensions and add a scalar potential. In addition to the event and
Cauchy horizons, when we complexify the radial coordinate, non-extremal black
holes will generically have other horizons as well. We prove that the product
of all of the horizon areas is independent of variations of the asymptotic
moduli further generalizing the attractor mechanism for extremal black holes.
In the presence of a scalar potential, as typically appears in gauged
supergravity, we find that the product of horizon areas is not necessarily the
geometric mean of the extremal area, however. We outline the derivation of
horizon invariants for stationary backgrounds.
