  Weyl semimetals are intriguing topological states of matter that support
various anomalous magneto-transport phenomena. One such phenomenon is a
negative longitudinal ($\mathbf{\nabla} T \parallel \mathbf{B}$)
magneto-thermal resistivity, which arises due to chiral magnetic effect (CME).
In this paper we show that another fascinating effect induced by CME is the
planar thermal Hall effect (PTHE), i.e., appearance of an in-plane transverse
temperature gradient when the current due to $\mathbf{\nabla} T$ and the
magnetic field $\mathbf{B}$ are not aligned with each other. Using
semiclassical Boltzmann transport formalism in the relaxation time
approximation we compute both longitudinal magneto-thermal conductivity (LMTC)
and planar thermal Hall conductivity (PTHC) for a time reversal symmetry
breaking WSM. We find that both LMTC and PTHC are quadratic in B in type-I WSM
whereas each follows a linear-B dependence in type-II WSM in a configuration
where $\mathbf{\nabla} T$ and B are applied along the tilt direction. In
addition, we investigate the Wiedemann-Franz law for an inversion symmetry
broken WSM (e.g., WTe$_{2}$) and find that this law is violated in these
systems due to both chiral anomaly and CME.
