We derive a new cross-property differential effective medium scheme for a composite material’s thermal conductivity as a function of its electrical conductivity and vice versa. Our scheme assumes that one phase is embedded in the other as inclusions. The relations are independent of inclusion volume fraction, but depend on the aspect ratio of the inclusions. We show that the method successfully models published laboratory measurements on a copper-graphite composite, with the inferred aspect ratio matching the physical shape of the inclusions. This work complements earlier results on elastic-electrical cross-property differential effective medium modelling, and has the potential to be extended for different cross-property relationships.