We have formulated the coupled transport of heat and hydrogen through a palladium membrane, including the dissociative adsorption of hydrogen at the surface. This was done using the systematic approach of non-equilibrium thermodynamics. We show how this approach, which deviates from Sieverts' law, makes is possible to calculate the direct impact that a temperature gradient, or a heat flux, has on the hydrogen flux. Vice versa, we show how the dissociative adsorption leads to heat sinks and sources at the surface. Using a set of transport coefficients estimated from experimental values available in the literature, calculations were performed. An enhancement of the hydrogen flux through the membrane with 10% and 25%, by transmembrane temperature differences of 24.8 K and 65.6 K, respectively, was predicted with a feed temperature of 673 K. Similarly, a transmembrane temperature difference of -176.5 K was observed to stop the hydrogen flux (Soret equilibrium). The calculations are done with estimated transport properties for the surfaces. The results show that an effort should be put into determination of these. Such experiments are discussed. (C) 2012 Elsevier B.V. All rights reserved.