The energy-dependent diffusion equation in the heavy gas approximation is considered for the case of a medium which has absolute temperature T1 in one halfspace and T2 in the other. The steady-state solution for F(x, E), the neutron flux per unit energy, is obtained in the absence of sinks and sources. Although the formal series solution diverges under certain conditions, it can be “summed” by means of the Euler transformation. Two approximation schemes giving simple analytical results are discussed. Numerical results for flux spectra and the total neutron density are presented for the case in which the temperature ratio is 2:1. The connection between this work and the theory of irreversible processes is briefly indicated.