  Thermodynamic potentials relevant to the micro-canonical, the canonical and
the grand-canonical ensembles, associated with rotating black holes in
D-dimensions, are analysed and compared. Such black holes are known to be
thermodynamically unstable, but the instability is a consequence of a subtle
interplay between specific heats and the moments of inertia and it manifests
itself differently in the different ensembles. A simple relation between the
product of the specific heat and the determinant of the moment of inertia in
both the canonical and the grand-canonical ensembles is derived. Myers-Perry
black holes in arbitrary dimension are studied in detail. All temperature
extrema in the micro-canonical ensemble are determined and classified. The
specific heat and the moment of inertia tensor are evaluated in both the
canonical and the grand-canonical ensembles in any dimension. All zeros and
poles of the specific heats, as a function of the angular momenta, are
determined and the eigenvalues of the isentropic moment of inertia tensor are
also found and classified. It is further shown that many of the thermodynamic
properties of a Myers-Perry black hole in D-2 dimensions can be obtained from
those of a black hole in D dimensions by sending one of the angular momenta to
infinity.
