Temperatures rise rapidly with altitude in the lower thermosphere. Somewhere above an altitude between 200 and 300 km (about 320 to 480 miles) the temperature stays pretty much constant across altitudes. However, the hottest temperature in the thermosphere varies a lot between day and night and between the minimum and maximum levels of solar activity during the Sun's 11-year sunspot cycle.
Images courtesy of The COMET Program and HAO at NCAR (modified by Windows to the Universe staff).