We employ a linearized full-wave model to show that the rovibrational damping (hereafter, RV damping) of gravity waves is an important source of atmospheric heating, which needs to be taken into account when modeling the wave processes in the jovian thermospheres. We find that RV damping of internal gravity waves becomes strong when the wave frequencies approach the thermal collision frequency. RV damping, compared to the damping by molecular viscosity and thermal diffusivity, can effectively lower the damping altitudes for waves with large frequencies, and requires larger upward wave energy fluxes to produce prescribed wave amplitudes for these waves. Particularly, the energy deposited by RV damping, viscous and thermal dissipation of the two waves identified in measurements by the Atmospheric Structure Instrument (ASI) on the Galileo Probe can produce a maximum temperature about 40 K higher than those in previous studies. We further demonstrate RV damping effect on the mesoscale gravity wave observed during the New Horizons flyby on Jupiter. Under the influence of RV damping, this wave has the vertical wavelength and damping altitude comparable to those of wave 2 retrieved from the ASI observations. The energy dissipation of these three observed waves, if coexist, should provide sufficient heating to produce the observed mean temperature between 357 km and 700 km above 1 bar.