Among a variety of characteristic features of the sonoluminescence phenomena, especially interesting is how high temperatures can be reached by a supersonic cavity. It is widely believed now that high temperatures such as 10[sup 5] K may be attained even under the experimental conditions of sonoluminescence. The dynamics of a supersonic cavity are simulated to determine the upper bound of temperatures reached by a gas content of the cavity. That is not to say that one should start with a realistic model to get quantitatively reliable results. To be specific, consider an air bubble in water. The compressibility of water, diffusion of air molecules through the bubble wall, condensation and evaporation of water, heat conduction, thermal radiation from a hot spot, phase transition from a gas to a plasma phase, and so on are taken into account. By use of the model, temperatures of the hot spot are calculated. Moreover, optimum values of supersonic parameters, i.e., amplitude and frequency, are searched for to get high hot-spot temperatures. Eventually the tendency is pointed out that the larger values of amplitude and in particular the smaller values of frequency are preferable to attain the higher temperatures. It is then concluded that there is a possibility of the temperatures reaching 10[sup 6] K or more.