In this study a model for the heat transfer into a single drop impacting onto a hot solid substrate in the film boiling regime is developed. The model accounts for the expansion of the thermal boundary layers in the spreading drop and in the solid substrate, and for the evaporation of the liquid phase, leading to the creation of a thin vapor layer. An explicit expression for thickness of the vapor layer is obtained from the energy balance at the liquid-vapor and vapor-solid interfaces. The theory allows prediction of the heat transferred from the hot substrate to the single drop during impact. This quantity is then used for the development of a model for an average heat transfer coefficient for spray cooling in the film boiling regime. The model accounts for the probability of drop interactions on the wall, when the droplet number density in the spray is high. The theoretical predictions for the heat transfer coefficient agree well with existing experimental data. (C) 2017 Elsevier Ltd. All rights reserved.