  The effective actions of a scalar and massless spin-half field are determined
as functions of the deformation of a symmetrically squashed three-sphere. The
extreme oblate case is particularly examined as pertinant to a high temperature
statistical mechanical interpretation that may be relevant for the holographic
principle. Interpreting the squashing parameter as a temperature, we find that
the effective `free energies' on the three-sphere are mixtures of thermal
two-sphere scalars and spinors which, in the case of the spinor on the
three-sphere, have the `wrong' thermal periodicities. However the free energies
do have the same leading high temperature forms as the standard free energies
on the two-sphere. The next few terms in the high-temperature expansion are
also explicitly calculated and briefly compared with the Taub-Bolt-AdS bulk
result.
