The transfer matrix method is used to solve the Milne problem for a half space for neutrons interacting with a moderator at temperature T. Two different scattering models are considered. They are (a) the free monatomic gas of arbitrary molecular mass with constant cross sections in the center-of-mass system, and (b) the Nelkin kernel for water. Both models permit an additional 1/v absorption cross section. We have obtained accurate numerical values for the diffusion length, the extrapolated end point, the critical absorption strength, and the boundary heating for a variety of values of the parameters. Comparison is made both with other calculations and with experiments.