The method proposed by Mooney and Steg (1969) for obtaining the dilatational dependence of the Gr¿neisen parameter from data on the pressure dependence of the thermal conductivity (or, equivalently, thermal diffusivity) is critically examined and applied to thermal diffusivity data for sodium chloride and quartz. The values obtained are &ggr;0' (≡d&ggr;/dΔ) ‖Δ=0) =3.0 for sodium chloride and &ggr;0'=2.0 for quartz. Corresponding values of the parameters q (≡&ggr;0'/&ggr;0) are 1.9 and 2.8, in reasonable agreement with values obtained by other methods. It is suggested that this method can be further investigated as a means of obtaining &ggr;0' and q from thermal data. A model for the lattice thermal conductivity of the mantle to the core boundary is presented. The model suggests that increases in conductivity with pressure due to lattice conduction processes in the mantle are less than 2.0%/kbar or 0.7%/km. Under conditions of normal geothermal gradient in the crust and upper mantle the increase in lattice conductivity due to the pressure effect will be substantially less than the decrease due to the temperature effect. A minimum value of lattice conductivity is attained in the region of the olivine-spinel phase change, 400 km. The lattice conductivity may be increase by a factor of 3 at the depth of the spinel-postspinel phase change owing to the high conductivity of the dense oxide phases. The lattice contribution to the thermal conductivity at the mantle-core boundary is ~0.01 cal/cm s ¿K.