The influence of a temperature-dependent rheology on large-scale continental extension is investigated using a thin viscous sheet model. A vertically averaged rheology is used that is consistent with laboratory experiments on power law creep of olivine and that depends exponentially on temperature. The behavior of the model depends principally on two parameters: the Peclet number, which describes the relative rates of advection and diffusion of heat, and a dimensionless activation energy, which controls the temperature dependence of the rheology. Numerical calculations of such a thin sheet subjected to an extensional boundary condition show the following results: At short times following the beginning of extension, deformation occurs with negligible change in temperature, so that only small changes in lithospheric strength occur due to attenuation of the lithosphere, and maximum rates of deformation are located close to the extensional boundary. However, after a certain time interval, thermal diffusion results in lowered temperatures in the lithosphere, strongly increasing lithospheric strength and slowing the rate of extension. This critical time depends principally on the Peclet number and is short compared with the thermal time constant of the lithosphere. The changes in strength cause the locus of high extensional strain rates to shift with time from regions of high strain to regions of low strain. Results of the calculations are compared with observations from the Aegean, where maximum extensional strains are found in the south, near Crete, but the largest present-day extensional strain rates occur about 300 km further north. The comparisons support the hypothesis that the observed separation of the loci of maximum strain and maximum present-day strain rates in the Aegean may be the consequence of changes in lithospheric strength arising from the temperature-dependent mechanical properties of lithospheric materials. ¿ American Geophysical Union 1989