  We consider CFTs conjectured to be dual to higher spin theories of gravity in
AdS_3 and AdS_4. Two dimensional CFTs with W_N symmetry are considered in the
lambda=0 (k --> infinity) limit, where they are conjectured to be described by
continuous orbifolds. The torus partition function is computed, using
reasonable assumptions, and equals that of a free field theory. We find no
phase transition at temperatures of order one; the usual Hawking-Page phase
transition is removed by the highly degenerate light states associated with
conical defect states in the bulk. Three dimensional Chern-Simons-matter CFTs
with vector-like matter are considered on T^3, where the dynamics is described
by an effective theory for the eigenvalues of the holonomies. Likewise, we find
no evidence for a Hawking-Page phase transition at large level k.
