This paper presents the results of mathematical modeling of the evaporation of a single water drop from the surface of a copper substrate using a new model, which does not require special experiments to close the system of equations and the corresponding boundary conditions with empirical constants. On the basis of the results of mathematical modeling, it was found that convective currents that occur in a small water drop (≤1 mm in diameter) do not significantly affect the characteristics or conditions of heat and mass transfer processes occurring in a liquid drop heated on a copper substrate. The results of numerical simulation showed that during the initial period of droplet heating, the latter undergoes a rapid transformation of the flow field. Five seconds after the beginning of the thermal action, a quasi-stationary regime of flows in the drop sets in. The model is tested on known experimental data. The theoretical analysis of temperatures at the characteristic points of a water drop and the surface on which the drop is located is carried out in ranges of thermal loads quite typical for practice, conditions for transferring heat and water vapor to the environment. According to the results of mathematical modeling, the possibility of using the developed model in the analysis of the state of cooling of surfaces heated to high temperatures, in cases typically used, is substantiated.