Anisotropic thermal diffusivity is examined in a cross-linked silicone elastomer deformed in simple elongation. Thermal diffusivity both parallel and perpendicular to the stretch direction is measured using an optical technique called forced Rayleigh scattering. The thermal diffusivity is found to increase linearly with stretch ratio to a value 10% larger than the equilibrium value for a stretch ratio of two. Measurements of the birefringence and tensile stress were used to evaluate the stress-optic rule, which was found to be valid. The difference between measured thermal diffusivities parallel and perpendicular to the stretch direction and tensile stress data were used to show the thermal conductivity and stress tensors are linearly related. These data appear to be the first direct evaluation of the stress-thermal rule in a deformed polymeric material.