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The temperatures in Jupiter's stratosphere, as measured by the Galileo Atmosphere Structure Instrument (ASI), show fluctuations that have been interpreted as gravity waves. We present a detailed description of these fluctuations, showing that they are not likely to be due to either measurement error or isotropic turbulence. These fluctuations share features with gravity waves observed in the terrestrial middle atmosphere, including the shape and amplitude of the power spectrum of temperature with respect to vertical wavenumber. Under the gravity wave interpretation, we calculate ranges of energy deposition and heat fluxes, place limits on the eddy Prandtl number, and compare predicted and observed eddy diffusion coefficients. We find that wave heating or cooling is likely to be important in Jupiter's upper stratosphere, that the Prandtl number lies between 1 and 4.4, and that diffusive filtering theory is a poor predictor of the eddy diffusion coefficient in Jupiter's atmosphere