The first measurement of the neutral temperature in the exosphere of Jupiter is reported. The observations were carried out by the Voyager 1 Ultraviolet Spectrometer during the solar occultation phase beginning 4.5 hours after the Jupiter encounter. The range of the exospheric temperature is found to be 1450-250+300 K. The uncertainty in the determination of the temperature appears to be largely a consequence of the lack of knowledge of the brightness distribution on the solar disc at the time of the observations. The high exospheric temperature appears to result from a combination of upward propagating inertia gravity waves, magnetospheric soft electrons and auroral electrons including those from the Io-plasma torus.