At first, the temperature gets warmer very quickly as you go upward in the thermosphere. After that, the temperature doesn't change much as you go higher. However, the hottest temperature changes between day and night. It also depends on how active the Sun is during its 11-year sunspot cycle. The thermosphere is hottest when the Sun is very active during "solar max". It isn't quite so hot when the Sun is less active during "solar min".
Images courtesy of The COMET Program and HAO at NCAR (modified by Windows to the Universe staff).