The analytical expression for the long-term variations of the exospheric temperature, T∞, has been derived by solving the simplified equation of the thermal balance and the hydrostatics equation. This expression describes the T∞ variations with the solar activity and season in a very good agreement with empirical and physical models. Excellent agreement has also been found between the exospheric temperatures calculated by the analytical expression and the physical model for the long-term cooling of the thermosphere due to the CO2 infrared radiation increase. Further analysis indicates that the T∞ long-term changes depend on the input energy, molecular thermal conductivity, and the temperature at the lower boundary of the thermosphere. The analytical expression makes it possible to compare the experimental data on the long-term cooling of the lower thermosphere and the exosphere. A strong discrepancy between these data has been revealed. ¿ 2000 American Geophysical Union