A kinetic model for droplet heating and evaporation into a high-pressure background gas (air) is described This model is based on the introduction of the kinetic region around evaporating droplets, where the dynamics of molecules are described in terms of the Boltzmann equations for vapor and air Both mass and heat transfer processes in this region are taken into account. The conditions at the outer boundary of the kinetic region are introduced by matching the mass fluxes of vapor leaving the kinetic region and entering into the surrounding hydrodynamic region and the corresponding heat fluxes. The new model is applied to calculations of heating and evaporation of fuel droplets in Diesel engine-like conditions. It is pointed out that in the case of droplet heating in a relatively cool gas (T-g = 750 K), the effect of nonzero heat flux in the kinetic region is negligible. This effect, however turns out to be important in the cases where gas temperature rises to 1000 and 1500 K. In the latter case, for droplets with initial radii equal to 5 mu m the predicted evaporation time in the presence of the heat flux in the kinetic region proves to be similar to 14% longer than predicted by the hydrodynamic model. The increase in this time in the case where the heat flux in the kinetic region is ignored would only be similar to 8%. The application of the rigorous kinetic model, taking into account the heat flux in the kinetic region, as described in this paper is recommended when accurate predictions of the values of droplet surface temperature and evaporation time are essential.