Abstract. We consider a random two-phase medium which represents a matrix containing an array of allowed to overlap spherical inclusions with random radii. A statistical theory of transport phenomena in the medium, on the example of heat propagation, is constructed by means of the functional (Volterra-Wiener) series approach. The functional series for the temperature is rendered virial in the sense that its truncation after the p-tuple term yields results for all multipoint correlation functions of the temperature field that are asymptotically correct to the order n², where n is the mean number of spheres per unit volume. The case p =2 is considered in detail and the needed kernels of the factorial series are found to the order n². In this way the full statistical solution, i.e., all needed correlation functions, and not only the effective conductivity, can be expressed in a closed form, correct to the said order.