Recent investigations of bubbly cavitating nozzle flows using the poltropic law for the partial gas pressure have shown flow instabilities that lead to flashing flow solutions. Here, we investigate the stabilizing effect of thermal damping on these instabilities. For this reason we consider the energy equation within the bubble, assummed to be composed of vapor and gas, in the uniform pressure approximation with low vapor concentration. The partial vapor pressure is fixed by, the vapor saturation pressure corresponding to the interface temperature, which is evaluated by, assumming the thin boundary laver approximation within the liquid. Consequently, the partial gas pressure is evaluated by its relation to the heat flux through the interface in the uniform pressure approximation. The model is then coupled to the stead-state cavitating nozzle flow equations replacing the polytropic law for the partial gas pressure. The instabilities found in steady cavitating nozzle flows are seen to be stabilized by thermal damping with or without the occurrence of bubbly shock waves.