  The thermodynamics of charged spherically symmetric AdS black holes in
conformal gravity is revisited using the recently proposed restricted phase
space (RPS) formalism. This formalism avoids all the bizarreness that arose in
the extended phase space formalism for this model. It is found that the charged
AdS black holes in this model may belong to a new universality class which is
different from all previously studied cases under the RPS formalism. Besides
the distinguished isocharge $T-S$ and isothermal $\Phi-Q_e$ behaviors, the
absence of Hawking-Page transition is another notable feature. On the other
hand, in the high temperature limit, the thermodynamic behavior of the present
model become exactly the same as that of the Einstein gravity and the black
hole scan models, which add further evidence for the universality of the
recently reported correspondence between high temperature AdS black holes and
low temperature quantum phonon gases in nonmetallic crystals.
