  We revisit the thermodynamic aspects of the scalar-tensor theory of gravity
in the Jordan and in the Einstein frame. Examining the {\it missing links} of
this theory carefully, we establish the thermodynamic descriptions from the
conserved currents and potentials by following both the Noether and the
Abbott-Deser-Tekin (ADT) formalism. With the help of conserved Noether current
and potential, we define the thermodynamic quantities, which we show to be {\it
conformally invariant}. Moreover, the defined quantities are shown to fit
nicely in the laws of (the first and the second) black hole thermodynamics
formulated by the Wald's method. We stretch the study of the conformal
equivalence of the physical quantities in these two frames by following the ADT
formalism. Our further study reveals that there is a connection between the ADT
and the Noether conserved quantities, which signifies that the ADT approach
provide the equivalent thermodynamic description in the two frames as obtained
in Noether prescription. Our whole analysis is very general as the conserved
Noether and ADT currents and potentials are formulated {\it off-shell} and the
analysis is exempted from any prior assumption or boundary condition.
