Brightness temperatures resulting from microwave thermal emission from a half-space random medium are calculated. The random medium has a nonuniform temperature profile and is characterized by correlation functions that possess both vertical and lateral variations. Radiative transfer equations are derived. They are solved with an iterative integral equation approach for small scattering albedo and with a numerical approach for general cases. New results are illustrated, discussed, and compared with various special cases. Phenomena caused by resonant scattering, which is absent under Rayleigh approximations, are revealed. Scattering in the lateral direction contributes to the decrease of the equivalent reflectivity and the increase of the brightness temperature.