An exact solution of the energy-dependent Boltzmann transport equation in the region near a temperature discontinuity is obtained for a nonabsorbing medium which is infinite in extent and has a temperature T1 in one half space and T2 in the other. The scattering cross section is assumed to be energy independent, and the scattering transfer kernel is represented by a degenerate-kernel approximation to the heavy-gas model. The method of solution is based upon a space-dependent thermalization theory developed earlier using the formalism of Case. Numerical calculations of both the scalar neutron flux and the total neutron density are included for various temperature ratios and neutron-to-moderator mass ratios. These results are compared with diffusion theory to assess the accuracy and range of validity of diffusion theory. For small temperature discontinuities, both diffusion theory and transport theory give very nearly the same value of the total neutron density at the interface. Away from the interface, a discrepancy between these theories becomes apparent because diffusion theory incorrectly predicts the energy-mode relaxation lengths, thus giving rise to an incorrect spatial dependence. Diffusion theory predicts the diffusion lengths accurately only when the energy exchange between the diffusing neutrons and the moderator material is weak. In addition, diffusion theory is found to become progressively less accurate for the higher energy modes. Thus, as the higher energy modes become more important, such as for a larger neutron-to-moderator mass ratio or for a larger temperature discontinuity, transport theory calculations of the neutron flux must replace the diffusion theory analysis.