A nonabsorbing heavy-gas model is used to study neutron thermalization in a moderator with a nonuniform temperature distribution. The method of Williams is first extended to arbitrary temperature distributions. The method is then applied to spherical geometry and numerical results are given for the mean energy of the neutrons. In the case where the radius of curvature of the temperature discontinuity is of the same order of magnitude as the rethermalization length, new transport-theoretical corrections are required to diffusion-theoretical results. In plane geometry, the P3 approximation is used to solve the Boltzmann equation and the mean energy of neutrons is calculated. Results are compared with diffusion-theoretical and exact calculations and agreement with the latter is found to be very satisfactory. Some neutron spectra are also plotted in the P3 approximation.