Models for conductive cooling of the lithosphere provide the foundation for interpretation of oceanic bathymetry and heat flow and consequently provide the basis for the currently accepted temperature structure of the oceanic lithosphere. These models are based upon average values for the thermal properties of olivine and pyroxene and do not account for any variation in these properties with temperature. In this paper a solution of the heat flow equation is presented that incorporates the observed variation of thermal diffusivity with temperature for olivine and pyroxene. The surface heat flow and bathymetry can vary with the square root of lithosphere age with variable diffusivity just as they do for a constant diffusivity solution, but the temperature structure is significantly different. Specifically, the temperature gradients and temperatures at shallow depths (about the 800 ¿C isotherm) obtained with the variable diffusivity model are less than those obtained with the averaged diffusivity model, whereas the temperature gradients at depths below the 800 ¿C isotherm are greater. Temperatures at a given depth within the mechanically strong portion of the lithosphere (<800 ¿C) are about 100 ¿C less using a variable diffusivity model, making this portion of the lithosphere thicker and the boundary with the asthenosphere more sharply defined mechanically as well as thermally. These changes reduce the effective elastic moduli interpreted from flexure of the lithosphere. ¿ American Geophysical Union 1992