>The space energy distribution of neutrons diffusing in a source-free, nonabsorbing medium possessing a temperature gradient is obtained by solving the appropriate Boltzmann equation to a second order approximation using the expansion technique of Chipman and Enskog. The medium is assumed to possess a locally Maxwellian energy distributlon and the neutron scattering is taken to be isotropic in the laboratory system of coordinates. It is found that the neutron current is increased in the direction of a negative temperature gradient and the thermal diffusion transport coefflcient is evaluated as a function of the mass of the moderator nuclei. For the case of infinite mass nuclei, the results correspond to the kinetic theory model of a Knudsen gas in a binary Lorentzian gas mixture. An analysis of the results is carried out in the framework of the thermodynamic theory of coupled irreversible processes. (auth)