In a series of experimental investigations Phillips and co-workers have determined the "Onsager heat of transport" in a cell with layers of a liquid and its vapor. Their results also include experimental observation of "cold to warm distillation", that is temperature difference driven mass transfer through the vapor from a cold to a warm liquid Mills and Phillips [e.g. C.T. Mills, L.F. Phillips, Distillation of a cool liquid onto a warmer surface, Chem. Phys. Lett. 372 (2002) 615-619]. Using standard irreversible thermodynamics for evaporation, condensation and transport, we present a theoretical analysis of the experimental set-up and discuss the reported measurements in terms of layer and interface properties. Necessary and sufficient criteria for a possible temperature difference driven cold to warm mass transfer are given. The criteria indicate that the occurrence of this phenomenon is highly unlikely. (C) 2012 Elsevier Ltd. All rights reserved.