To estimate the effective conductivity of gas-filled porous media the standard micromechanical approach based on the classical mechanics of continuum media is usually applied. If the characteristic size of inhomogeneities is comparable with the mean free path of gas molecules, the classical equations of thermal conductivity are not applicable. In this case, in order to describe the gas behavior it is necessary to use methods of physical kinetics and rarefied gas dynamics. In this work we have considered so-called slip flow regime, 0 < Kn << 1, where Kn = lambda/l is the Knudsen number; lambda is the mean free path of gas molecules; 1 is the characteristic pore size. In this regime, we can use the classical equations of mechanics of continuum media with modified boundary conditions that take into account the temperature and energy flux jumps on the pore boundaries. We have solved the so-called one-particle problem of thermal polarization of gas-filled and solid inclusions suspended in the gas. We have used these solutions in some self-consistent homogenization methods to calculate the effective conductivity coefficient. The calculations performed have shown that the effective conductivity of gas-solid mixtures depends substantially on the pore size (or the Knudsen number). (C) 2016 Elsevier Ltd. All rights reserved.