Within the framework of the assumptions that the processes of condensation or evaporation in subcooled or superheated liquids are controlled by convective heat transfer, and that the flow past a spherical bubble of a changeable radius is both potential and axisymmetric, the heat exchange of a vapor bubble at high Nusselt numbers is considered. Asymptotic expressions for the Nusselt number, taking into account the unsteady character of the thin thermal boundary layer due to the changeability of the bubble radius and the relative velocity, are obtained. Calculations and comparisons between the present theory and previous numerical and experimental data are performed.