Radiative heat transfer through insulation can be affected both by scattering of thermal radiation from the solid phase of the insulation and by absorption of radiant energy within the insulation, with, in the latter case, an attendant change in temperature and re-radiation of energy. For insulation in which there is heat transfer by both conduction and radiation, the temporal variation of heat flow can be quite different for the case where the radiative transfer is controlled by scattering than it is for the case where the radiative transfer involves absorption and re-radiation. In this paper, analytical solutions and numerical analyses are presented for several one-dimensional cases with temperature-versus-time boundary conditions. The results clearly show that if part of the heat transfer through a medium is by direct or scattered radiation, predictions of heat flow that are based upon conventional conductive heat transfer analyses can be drastically in error. In addition, it is shown that transient thermal tests on such (scattering) media do not yield proper thermal diffusivity values.