The upward motion of rock masses near the Earth's surface is accompanied by changes in temperature, and so the unroofing history of nearly every major mountain belt on earth has been accurately measured using thermochronologic techniques. More fundamental to continental dynamics, however, is resolving the motion of the Earth's surface with respect to the geoid. Constraining these motions has remained elusive because variations in temperature at the Earth's surface, while dependent on elevation, are not resolvable using traditional thermochronologic methods. We introduce a new technique for estimating the time of topographic uplift of a mountain range by mapping out the low-temperature thermal structure imparted by river incision using UTh/He ages of apatites. Our first results from the southern Sierra Nevada, U.S.A., suggest that the two largest transverse rivers in the range had cut deep canyons by 80 Ma. The data require significant topographic relief at that time, contrary to previous studies suggesting the range was a low-standing plateau prior to Late Cenozoic uplift. The technique exploits the fact that horizontal variations in temperature in the uppermost part of the continental lithosphere will result from the development of orogen-normal river drainages along the edge of a mountain belt or plateau. This structure results in cooling of samples collected beneath ancient river valleys faster than those collected at the same structural level beneath intervening ridges (Fig. 1). If broad constraints on the unroofing rate and geotherm are available, the age difference between valleys and ridges may be used to estimate paleorelief, and therefore the minimum height of a mountain range, at some time in the past. Assuming nominal values for the geotherm and soil lapse rate, the amplitide of horizontal temperature variation near the Earth's surface ranges from ~10-80~ for relief of 1 -3 kin. Neglecting lateral variations in reduced heat flux, radioactive heat production, mean surface temperature and advection of heat due to erosion, the temperature T below a