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We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS3 and AdS4. Two-dimensional CFTs with WN symmetry are considered in the λ = 0 (k → ∞) 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 1; 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 T³, 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 a large level k. [ABSTRACT FROM AUTHOR]