The conventional method of calculating atmospheric temperature profiles using Rayleigh-scattering lidar measurements has limitations that necessitate abandoning temperatures retrieved at the greatest heights, due to the assumption of a pressure value required to initialize the integration at the highest altitude. An inversion approach is used to develop an alternative way of retrieving nightly atmospheric temperature profiles from the lidar measurements. Measurements obtained by the Purple Crow lidar facility located near The University of Western Ontario are used to develop and test this new technique. Our results show temperatures can be reliably retrieved at all heights where measurements with adequate signal-to-noise ratio exist. A Monte Carlo technique was developed to provide accurate estimates of both the systematic and random uncertainties for the retrieved nightly average temperature profile. An advantage of this new method is the ability to seed the temperature integration from the lowest rather than the greatest height, where the variability of the pressure is smaller than in the mesosphere or lower thermosphere and may in practice be routinely measured by a radiosonde, rather than requiring a rocket or satellite-borne measurement. Thus, this new technique extends the altitude range of existing Rayleigh-scatter lidars 10-15 km, producing the equivalent of four times the power-aperture product.