The paper focuses on the concept of equivalent isotropic microstructure, formed by randomly oriented oblate spheroids of certain distribution over the aspect ratios, that produces the same effective thermal conductivity as the real one. Such a microstructure is independent of the properties of the inhomogeneities (although it depends on their volume fractions of the constituents). We propose a methodology to identify it using Maxwell homogenization technique which seems to be less contradictory than the others. We first verified the proposed approach on numerical examples and showed that the equivalent microstructure cannot be constructed independently on the porosity. Then we illustrated the applicability of the proposed methodology to evaluation of the equivalent microstructure of porous sandstone at different levels of porosity.