The microwave radiometric temperature of heterogeneous materials is altered by internal scattering. Radiative transfer theory and a Rayleigh scattering model are used to obtain the microwave temperature and its polarization as a function of view angle for emission from a nonuniformly thick layer containing scatterers. The scatter-induced change in brightness temperature is generally negative and may be many tens of degrees. There are situations, however, such as the emission from ice over freshwater, where the scatterers may increase the brightness temperature by as much as 30¿C. Lunar microwave temperatures may be decreased from a few degrees to more than 50¿C depending upon wavelength and upon the specific lunar target; the brightness temperature as a function of wavelength of a lava flow may be decreased from 1¿C to more than 30¿C by near-surface vesicles; snow may appear from a few degrees to more than 60¿C darker as it ages; and air bubbles in ice over freshwater may increase the brightness temperature by as much as 30¿C or decrease it by as much as 50¿C depending upon the thickness of the ice and the size and concentration of the bubbles.