  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.
