The Atmosphere Structure Instrument on the Galileo probe detected wavelike temperature fluctuations superimposed on a 700-kelvin temperature increase in Jupiter’s thermosphere. These fluctuations are consistent with gravity waves that are viscously damped in the thermosphere. Moreover, heating by these waves can explain the temperature increase measured by the probe, This heating mechanism should be applicable to the thermospheres of the other giant planets and may help solve the long-standing question of the source of their high thermospheric temperatures.