The heating and vaporization of a pure cold fluid package in a hot environment of the same fluid has been analyzed. The model applies to subcritical as well as supercritical fluid conditions and relies on the assumption of constant pressure and quasisteady conditions in the gas phase (in a reference system receding with the cold front). An asymptotic analysis is performed using the ratio of the hot fluid density to the density of the cold fluid package as the smallness parameter. Then, a transcendental equation is obtained which provides the evolution of the cold package radius. For longer times when isothermal conditions are achieved in the cold region, the d(2) law is obtained. Some deviations from this law, due to the unsteadiness of the heating process in the cold region, are evaluated and discussed.