The unsteady spherically symmetrical evaporation of a cold single-component droplet in atmospheres at pressures above the critical pressure of the liquid and at temperatures above the critical temperature of the liquid is modelled. High pressure phase equilibrium is assumed at the droplet surface, and solubility of the ambient gas in the droplet, temperature and composition inhomogeneities within the droplet, real gas effects and variable property effects are considered. Depending on the ambient conditions, the droplet surface reaches the critical state and vanishes. Thereafter, a pure diffusion problem is treated.