  In this work we investigate the thermodynamic properties of conformal gravity
in four dimensions. We compute the \emph{area(or entropy) functional} relation
for this black hole. We consider both de-Sitter (dS) and anti de-Sitter (AdS)
cases. We derive the \emph{Cosmic-Censorship-Inequality} which is an important
relation in general relativity that relates the total mass of a spacetime to
the area of all the black hole horizons. Local thermodynamic stability is
studied by computing the specific heat. The second order phase transition
occurs at a certain condition. Various type of second order phase structure has
been given for various values of $a$ and the cosmological constant $\Lambda$ in
the Appendix. When $a=0$, one obtains the result of Schwarzschild-dS and
Schwarzschild-AdS cases. In the limit $aM<<1$, one obtains the result of
Grumiller space-time. Where $a$ is non-trivial Rindler parameter or Rindler
acceleration and $M$ is the mass parameter. The \emph{thermodynamic volume
functional} relation is derived in the \emph{extended phase space}, where the
cosmological constant treated as a thermodynamic pressure and its conjugate
variable as a thermodynamic volume. The \emph{mass-independent} area (or
entropy) functional relation and thermodynamic volume functional relation that
we have derived could turn out to be a \emph{universal} quantity.
