The unsteady heat transfer characteristics of a Stirling engine regenerator have been theoretically studied. The matrix of the regenerator was assumed to be a homogeneous continuum which absorbs and emits thermal radiation. The coupled energy equations for gas and matrix were solved taking account of conductive, convective and radiative heat transfer. The thermal response of the regenerator has been clarified for a wide range of incident radiation, frequency, gas velocity, and heat capacity ratio. It has been demonstrated that the incident radiation and gas-phase conduction exert considerable influence on the gas and matrix temperatures, and thus on the temperature efficiency of the regenerator.