  We explore the consequences of a time-dependent inflaton Equation-of-State
(EoS) parameter in the context of the post-inflationary perturbative Boltzmann
reheating. In particular, we numerically solve the perturbative coupled system
of Boltzmann equations involving the inflaton energy density, the radiation
energy density and the related entropy density and temperature of the produced
particle thermal bath. We exploit reasonable Ans\"atze for the EoS and discuss
the robustness of the Boltzmann system. We also comment on the possible
microscopic origin related to a time dependent inflaton potential, discussing
the consequences on a preheating stage and the related (primordial)
gravitational waves.
