In thick continental lithosphere, the time-scale for diffusive heat transport is comparable to the half-lives of Uranium, Thorium and Potassium, implying that temperatures are not in equilibrium with the instantaneous rate of radiogenic heat generation. Solving the heat equation with decaying heat sources leads to a vertical temperature profile which exhibits significant curvature and which may be hotter than a steady-state profile by as much as 150K. Applying a steady-state thermal model to xenolith (P, T) data leads to an overestimate of the mantle heat flow. The lithospheric mantle undergoes secular cooling even when thermal conditions at the base of the lithosphere remain steady. Predicted cooling rates are in the range of 50--150 K Ga-1, close to values reported recently for mantle xenoliths from the Kaapvaal craton, South Africa. Time-dependent thermal models depend explicitly on, and hence allow new constraints on, lithosphere thickness.