Thermal diffusivity measurements of seven naturally deformed upper mantle rocks were made as a function of pressure (up to 1 GPa), temperature (up to 1250 K), and the deformation fabric of the samples. For each sample the strain-induced crystal preferred orientations of olivine and pyroxenes were measured, and petrophysical models, based on the thermal diffusivity tensors of the olivine and enstatite crystals, were used to evaluate the three-dimensional distribution of the thermal diffusivity. Both model predictions and measurements show that the anisotropy of thermal diffusivity remains large at the rock scale: 15--28%, depending on the strength of the olivine crystallographic fabric. The direction of maximum thermal diffusivity is parallel to the lineation (flow direction), and the minimum of thermal diffusivity is normal to the foliation plane (flow plane). This anisotropy is preserved at high temperature and pressure. However, measured thermal diffusivities are 20--30% lower than model predictions. This discrepancy between measurements and model predictions cannot be explained by the presence of cracks in the samples because the closure of these void spaces, evaluated through the high-pressure experiments, is found to have a negligible effect on measured thermal diffusivities. Thermal diffusivity for all samples displays a weak linear dependence on pressure of ~10% GPa-1. Thermal diffusivities observed in the high-temperature experiments (1000--1250 K) are compatible with a weak radiative contribution to the total heat diffusion.