  In this paper, we discuss the effect of a periodically driving circularly
polarized laser beam in the high frequency limit, on the band structure and
thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We
develop the notion of an effective Fermi surface stemming from the
time-averaged Floquet Hamiltonian and discuss its effects on the steady-state
occupation numbers of electrons and holes in the linearized model. In order to
compute the transport coefficients averaged over a period of the incident laser
source, we employ the Kubo formalism for Floquet states and show that the Kubo
formula for the conductivity tensor retains its well known form with the
difference that the eigenstates and energies are replaced by the Floquet states
and their quasi-energies. We find that for type-I WSMs the anomalous thermal
Hall conductivity grows quadratically with the amplitude $A_{0}$ of the U(1)
gauge field for low tilt, while the Nernst conductivity remains unaffected. For
type-II WSMs, the Hall conductivity decreases non-linearly with $A_{0}$ due to
the contribution from the physical momentum cutoff, required to keep finite
electron and hole pocket sizes, and the Nernst conductivity falls of
logarithmically with $A_{0}^2$. These results may serve as a diagnostic for
material characterization and transport parameter tunability in WSMs, which are
currently the subject of a wide range of experiments.
