  Criteria for thermal stability of charged rotating black holes of any
dimension are derived, for horizon areas that are large relative to the Planck
area (in these dimensions). The derivation is based on generic assumptions of
quantum geometry based on some results of loop quantum gravity, and equilibrium
statistical mechanics of the Grand Canonical ensemble. There is no explicit use
of classical spacetime geometry in this analysis. The only assumption is that
the mass of the black hole is a function of its horizon area, charge and
angular momentum. Our stability criteria are then tested in detail against
specific classical black holes in spacetime dimensions 4 and 5, whose metrics
provide us with explicit relations for the dependence of the mass on the charge
and angular momentum of the black holes. This enables us to predict which of
these black holes are expected to be thermally unstable under Hawking
radiation.
