We have employed Direct Non-Equilibrium Molecular Dynamics (NEMD) simulations to compute the thermal conductivity and the thermal diffusion coefficient alpha(T) in a methane-n-decane binary mixture in the liquid state. We discuss the choice of a non-equilibrium molecular dynamics method rather than the equilibrium method using Green-Kubo integrals. We emphasize the fact that using direct-NEMD, there is no need for additional calculation of any thermodynamic property of the mixture. The n-decane molecules are realistically modelled as flexible bodies and using the Anisotropic United Atoms (AUA) interaction scheme of Toxvaerd. The statistical uncertainty for the thermal conductivity is less than 1% and that for the thermal diffusion factor is about 5%. We show that the thermal conductivity results agree with predictions from Assael. The thermal diffusion data are in accordance with the empirical relationships of Kramers and Breeder and experimental results, where available. (C) 1998 Elsevier Science B.V. All rights reserved.