The article presents the results of an experimental comparison of methane transport in the pore structure of a membrane catalyst under isothermal and non-isothermal Knudsen diffusion conditions. It is shown that under the conditions of non-isothermal Knudsen diffusion in the pore structure of the membrane catalyst, there is a coupling of dry reforming of the methane (DRM) and gas transport, which leads to the intensification of this process. The reasons for the intensification are changes in the mechanism of gas transport, an increase in the rate of mass transfer, and changes in the mechanism of some stages of the DRM. The specific rate constant of the methane dissociation reaction on a membrane catalyst turned out to be an order of magnitude (40 times) higher than this value on a traditional (powder) catalyst.