The thermal diffusivity of the La-doped layered perovskite Sr2Nb2O7 parallel and perpendicular to the perovskite layers is reported from room temperature up to 1000 degrees C. The anisotropy persists through an incommensurate-normal ferroelectric phase transformation at 215 degrees C and up to 1000 degrees C, the maximum temperature of our measurements. The thermal conductivity perpendicular to the perovskite layers, derived from the diffusivity in the same direction, calculated using the density and measured heat capacity, has a constant value of 1.05 +/- 0.05 W/mK up to 1000 degrees C. Possible explanations for the low thermal conductivity and anisotropy are described.