Anisotropic thermal transport in cross-linked polybutadienes deformed in simple elongation is investigated experimentally. Using a novel optical technique based on forced Rayleigh scattering, two components of the thermal diffusivity tensor are measured as a function of stretch ratio. The thermal diffusivity is found to increase in the direction parallel, and decrease in the direction perpendicular, to the stretch direction, with a maximum anisotropy of similar to 25% relative to the equilibrium value. Measurements of the tensile stress as a function of stretch ratio were also made. These data were used to show that the thermal conductivity and stress tensors are linearly related or that the stress-thermal rule is valid. The value of the stress-thermal coefficient for the crosslinked polybutadiene systems was found to be consistent with previously reported values for both a cross-linked silicone rubber and polyisobutylene melts.