  In a recent experiment, a Bose-Einstein condensate was trapped in an
anharmonic potential which is well approximated by a harmonic and a quartic
part. The condensate was set into such a fast rotation that the centrifugal
force in the corotating frame overcompensates the harmonic part in the plane
perpendicular to the rotation axis. Thus, the resulting trap potential became
Mexican-hat shaped. We present an analysis for an ideal Bose gas which is
confined in such an anharmonic rotating trap within a semiclassical
approximation where we calculate the critical temperature, the condensate
fraction, and the heat capacity. In particular, we examine in detail how these
thermodynamical quantities depend on the rotation frequency.
