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The conductive heat transfer in the three-dimensional medium water–air–solid grain was investigated on the basis of the exact analytical solution of the problem on the steady harmonic 2D temperature field in a composite having a doubly periodic chequered structure in the form of an isogonal tiling. An explicit expression for the diffusivity of the indicated composite depending on its volumetric moisture content has been constructed. It was established that the diffusivity of this composite reaches a physically meaningful maximum at a certain degree of its saturation with water. It is shown that the expression obtained is analogous to the solution of the classical Muscat problem on the filtration of oil in a doubly periodic array of production and injection wells. [ABSTRACT FROM AUTHOR]