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Electromagnetic (EM) heat exchangers (HX) are systems that convert EM energy into heat or mechanical work. One potential design consists of a porous lossy ceramic material heated by EM waves with a compressible gas coolant. EM heating of ceramics is nonlinear, since the loss factor is temperature dependent. Designing such EM HXs requires an understanding of coupling between temperature, the electric field, and gas dynamics at the pore scale. To mimic this microscale phenomenon, a single channel with a high-speed gas coolant in perfect thermal contact with a thin solid ceramic layer is considered, with an applied plane-wave electric field propagating normal to the channel walls. From a thin-domain asymptotic analysis, the conservation laws reduce to a Rayleigh flow in the gas coupled with averaged thermal energy conservation equations at leading order. The model predicts that the kinetic energy of the gas increases up to 12.5 times the inlet value when thermal runaway occurs in the ceramic region for the cases considered, and thermal choking is possible when the coolant reaches the sonic state. Local maxima of efficiency occur on a discrete set of ceramic thicknesses that correspond to Fabry–Bragg resonances of the electric field. [ABSTRACT FROM AUTHOR]