This article presents an analysis of kinetic studies of dry methane reforming (DRM) in a reactor with a membrane catalyst (RMC) in the modes of a contactor with “diffusion” and “forced” mass transfer. Comparison of the specific rate constants of the methane dissociation reaction in membrane and traditional reactors confirmed the phenomenon of intensification of dry methane reforming in a membrane catalyst (MC). It has been experimentally established that during DRM, a temperature gradient arises in the channels of the pore structure of the membrane catalyst, characterized by a decrease in temperature towards the inner volume of the MC, and initiates the phenomenon of thermal slip. The features of this phenomenon are highlighted and must be considered in the analysis of kinetic data. The main provisions of the hypothesis explaining the effect of intensification by the occurrence of thermal slip in the channels of the pore structure of the MC are formulated. The proposed hypothesis, based on thermal slip, explains the difference in rate constants of traditional and membrane catalysts, and substantiates the phenomenological scheme of DRM stages in a reactor with a membrane catalyst.