  In the paper we further refine the thermodynamics method of black hole/CFT
correspondence. We show that one can derive the central charges of different
holographic pictures directly from the entropy product $S_+S_-$ if it is
mass-independent, for a black hole in the Einstein gravity or the gravity
without diffeomorphism anomaly. For a general black hole in the Einstein
gravity that admits holographic descriptions, we show that the thermodynamics
method and asymptotic symmetry group (ASG) analysis can always give consistent
results in the extreme limit. Furthermore, we discuss the relation between
black hole thermodynamics and the hidden conformal symmetry. We show that the
condition $T_+A_+=T_-A_-$, with $A_\pm$ being the outer and inner horizon
areas, is the necessary, but not sufficient, condition for a black hole to have
the hidden conformal symmetry. In particular, for the Einstein(-Maxwell)
gravity $T_+A_+=T_-A_-$ is just the condition $T_+S_+=T_-S_-$, with $S_\pm$
being the outer and inner horizon entropies, which is the condition for the
entropy product $S_+S_-$ being mass-dependent. When there exists the hidden
conformal symmetry in the low-frequency scattering off the generic non-extremal
black hole, it always leads to the same temperatures of dual CFT as the ones
got from the thermodynamics method.
