  We revisit the study of the phase structure of higher spin black holes
carried out in arXiv$:1210.0284$ using the "canonical formalism". In particular
we study the low as well as high temperature regimes. We show that the
Hawking-Page transition takes place in the low temperature regime. The
thermodynamically favoured phase changes from conical surplus to black holes
and then again to conical surplus as we increase temperature. We then show that
in the high temperature regime the diagonal embedding gives the appropriate
description. We also give a map between the parameters of the theory near the
IR and UV fixed points. This makes the "good" solutions near one end map to the
"bad" solutions near the other end and vice versa.
