The heat transfer through a plane layer of a semitransparent solid is investigated experimentally for conditions under which the radiative transport must be considered. Temperature profiles measured with a Mach-Zehnder interferometer and the total heat flux are compared to rigorous analysis employing a rectangular multiband model of the spectral-absorption coefficient and simplified approximate techniques. Results for opaque and semitransparent boundary conditions are presented for three sample thicknesses. Fused quartz is employed for the specimen, as its thermophysical properties are similar to those of several materials which are commonly exposed to severe thermal conditions, it has excellent high-temperature and interferometric properties, and its strong infrared absorption peak serves as a critical test of a band model. For the experimental conditions which are considered, it is shown that the coupling of conduction and radiation cannot be neglected for the prediction of the heat transfer, although no appreciable influence on the temperature profile was observed. Approximate analytical techniques are shown to be accurate in this situation.