Thermal diffusivities of fluid water have been measured to a pressure of 3.5 GPa, a density of 1.4 g cm-3 and a temperature of 400 degreesC. Above 100 degreesC, both the diffusivities and the related conductivities are found, unexpectedly, to scale as the square-root of absolute temperature; in contrast, the excess conductivities are highly dependent on temperature. Measurements at 25 degreesC, extending into a metastable regime with respect to ice VI, do not scale in this manner and this anomalous behavior is not suppressed by pressures up to 1.3 GPa.