The previously developed kinetic model for droplet heating and evaporation into a high pressure air is generalised to take into account the combined effects of inelastic collisions between molecules in the kinetic region, a non-unity evaporation coefficient and temperature gradient inside droplets. It is pointed out that for the parameters typical for Diesel engine-like conditions, the heat flux in the kinetic region is a linear function of the vapour temperature at the outer boundary of this region, but practically does not depend on vapour density at this boundary for all models, including and not including the effects of inelastic collisions, and including and not including the effects of a non-unity evaporation coefficient. For any given temperature at the outer boundary of the kinetic region the values of the heat flux are shown to decrease with increasing numbers of internal degrees of freedom of the molecules. The rate of this decrease is strong for small numbers of these degrees of freedom but negligible when the number of these degrees exceeds 20. This allows us to restrict the analysis to the first 20 arbitrarily chosen degrees of freedom of n-dodecane molecules when considering the effects of inelastic collisions. The mass flux at this boundary decreases almost linearly with increasing vapour density at the same location for all above-mentioned models. For any given vapour density at the outer boundary of the kinetic region the values of the mass flux are smaller for the model, taking into account the contribution of internal degrees of freedom, than for the model ignoring these degrees of freedom. It is shown that the effects of inelastic collisions lead to stronger increase in the predicted droplet evaporation time in Diesel engine-like conditions relative to the hydrodynamic model, compared with the similar increase predicted by the kinetic model considering only elastic collisions. The effects of a non-unity evaporation coefficient are shown to be noticeable for gas temperatures of 1500 K. The application of the rigorous kinetic model, taking into account the effects of inelastic collisions and a non-unity evaporation coefficient, and the model taking into account the temperature gradient inside droplets, is recommended when accurate predictions of the values of droplet surface temperature and evaporation time in Diesel engine-like conditions are essential. © 2012 Elsevier Ltd. All rights reserved.