The generation of ultrasound in a porous water-saturated medium subjected to rapid electromagnetic heating is considered. The irradiation provides the Joule heating of narrow and electrically high resistive pore throats, which interconnect cavities within the medium and, consequently, determine the permeability of the medium. Because of the small throat sizes, the sound generation is accompanied by considerable thermal flows going out from the throats into a relatively cold environment. Due to the latter, the output of the ultrasonic measurement allows one to estimate the rate of the thermal exchange process. A common geometric model of fluid flows and electric currents throughout a complicated network of intergranular cavities and their interconnecting throats is used for calculating the permeability of a rock on the basis of the determined values of the thermal exchange rate.