Radiation heat transfer within a high-temperature solar thermochemical reactor that features two cavities in series is considered. The inner cavity is subjected to concentrated solar radiative power entering through a spectrally selective window positioned at its aperture. The outer cavity is a well-insulated enclosure containing the inner cavity. It serves as the reaction chamber and is subjected to thermal radiation emitted from the inner cavity A radiation heat transfer analysis based on the radiosity enclosure theory is formulated and solved using the gray-band approximation for the selective (quartz) window Energy absorption efficiencies and temperatures are determined and compared to the windowless case.