The thermal diffusivity of fluid oxygen in the diamond-anvil cell has been measured from 1 to 12.6 GPa and 25 to 300 degrees C. These constitute the first experimental measurements of thermal transport properties of simple fluids above 1 GPa. Diffusivities are found to rise sharply from a minimum at intermediate pressures and then to level off at similar to 6 GPa. Thermal conductivities derived from these measurements do not vary as root T, rather the excess conductivities are approximately independent of temperature. The diffusivities of nitrogen, previously measured to 1 GPa, closely match those of oxygen when scaled as suggested by a simple, corresponding states theory.