Thinning of the lithosphere by heat carried convectively to its base is possible mechanism for the initation of continental rifting. The lithosphere-asthenosphere boundary marks the transition from a quasi-rigid behavior of the mantle on geological time scales to a viscous one. The boundary lies at or close to the solidus of the mantle material and its position is a function of temperature and pressure. Additional heat carried to the boundary will cause it to rise and the lithosphere to thin. A one-dimensional model is used to study the upward movement of the boundary from an initial equilibrium position as a consequence of an increase in the heat flux from the convecting mantle. The ratio of the amount of thinning to the initial thickness is directly proportional to the increase in heat flux from the asthenosphere and inversely proportional to the difference between the final subcrustal geothermal gradient and the slope of the transition temperture profile. The rate of thinning is determined by the initial and final equilibrium thicknesses, the thermal diffusivity, the transition temperature profile and the plume temperature profile. It depends only slightly on any latent heat associated with the lithosphere-asthenosphere transition. During a large fraction of the time between the initial and final equilibrium states, the lithosphere thins at a rate which is inversely proportional to the square root of time t. Even 300-km-thick lithospheres may be thinned to 50 km or crustal thicknesses in tens of million years by the heat advected by mantle plumes. This heat contributes to an enhanced surface heat flow. Because of the constant level of radioactive heat production in the crust, the ratio of the final to the initial surface heat flow increases much less than the ratio of the final to the initial heat flow from the asthenosphere. For large increases in asthenospheric heat flow, the lithosphere is almost thinned to the crust before any significant change of surface heat flow occurs. Uplift due to thermal expansion upon lithospheric thinning is of the order of 102--103 m. A Rayleigh-Taylor instability acting on the thinning lithosphere may further increase thinning rates and cause magmatic intrusions of the lithosphere and surface volcanism.