Thermodynamics of a single bag is examined in detail in order to obtain new information on the properties of the phase transition between hadronic matter and quark-gluon plasma. With the zero point energy term added to the usual thermodynamical terms, our formalism provides a smooth interpolation between a ground state bag (a lowest-lying hadron) at zero temperature and an excited bag at a critical temperature. In the simplest case where there is no surface energy, the bag radius diverges like (T c −T)−1/4 as the temperatureT approaches the critical temperatureT c from below, implying a second order transition into the quark deconfining phase at higher temperature. If there is negative surface energy, the bag radius diverges like (Tc−T)−1. If the surface energy is positive, the radius approaches a finite value asT goes to another critical temperatureT 2c (>T c ) and there is no finite radius solution forT>T 2c , indicating a first order phase transition. The temperature-dependence of both the internal energy and the free energy is examined in connection with the problem of mass shift of hadrons at high temperature. Virial theorems play an important role. Effects of the quark chemical potential are discussed briefly.