The addition of impurities affects both the lattice and electronic thermal conductivities of a semiconductor. At high temperatures the lattice resistance is increased by an amount independent of temperature: for the small concentrations normally present in semiconductors the impurity resistance can be derived very simply from the variational principle. The electronic contribution is normally obtained from the electrical conductivity via a Lorentz number. For a degenerate electron gas assuming polar scattering dominates an approximate calculation shows that at high temperatures the Lorentz number can be considerably reduced below the standard' value g0= (π2/3)(k/e)2. These theoretical calculations do not completely agree with the observed conductivity of impure In As between 300 and 700°K (Stuckes 1960). The disagreement is attributed to the electronic contribution. To give agreement the Lorentz number would have to be reduced further but the precise amount is uncertain owing to experimental errors.