Flow-induced anisotropic thermal conduction in a polyisobutylene melt subjected to shear deformations is studied experimentally. Time-dependent measurements of the full (four components) thermal diffusivity tensor following step shear strain flow are presented. These data were obtained with a novel experimental setup based on the optical technique of forced Rayleigh scattering. Birefringence and stress measurements are made for the same flow, and the well-known stress-thermal rule is found to be satisfied. Thermal diffusivity data and stress data are used to test directly the stress-thermal rule, which is also satisfied for the two cases considered. Consideration of stress-thermal coefficients from the present and previous studies gives preliminary evidence that flow-induced anisotropic thermal conduction is a universal phenomenon for flexible polymers.