An electromagnetic (EM) heat exchanger (HX) converting EM energy into heat or mechanical work acts as a receiver end in high power-beaming applications. One potential design of an EM HX consists of a porous ceramic material, which is heated by EM waves, and a compressible gas coolant that delivers energy from the porous media to the outlet. The ceramic materials of interest absorb energy from the EM waves better as temperature increases, that can lead to extremely rapid temperature rises known as thermal runaway. Modeling such an EM HX requires an understanding of the gas dynamics taking place at the pore-scale when coupled with the phenomenon of thermal runaway. To capture the pore-scale gas dynamics, we consider a 2D thin and long structure with a channel carrying a pressure-driven ideal gas flow in perfect thermal contact with a thin ceramic layer. We derive two thin-domain asymptotic models: with and without thermal diffusion along the flow direction, each of which is solved numerically. We find that when local onset of thermal runaway takes place in the ceramic, diffusion along the flow direction at the microscale cannot be ignored. Unlike models of EM HX found in the literature, this work includes thermal expansion done by the gas at the microscale. By looking at temperature profiles at the steady-state, we show that Joule-Thompson cooling of the gas occurs locally when work done by the gas dominates.