New solutions to the droplet heat conduction equation, assuming that the droplet radius is a linear function of time, are described alongside new solutions to the same equation, assuming that the time evolution of droplet radius Rd(t) is known. For sufficiently small time steps the time evolutions of droplet surface temperatures and radii, predicted by both approaches for typical Diesel engine-like conditions, coincide. Both solutions predict lower droplet temperatures and slower evaporation when the effects of the reduction of Rd(t) due to evaporation are taken into account. A simplified model for multi-component droplet heating and evaporation, based on an analytical solution to the species diffusion equation, is discussed. This model has been generalised to take into account the effect of coupling between the droplets and the surrounding gas. A new approach to modelling multi-component droplets, including large numbers of components, heating and evaporation is discussed. This new approach is based on the replacement of a large number of actual components with a small number of quasi-components. The evaporation and condensation of n-dodecane (C12H26) are investigated using the molecular dynamics (MD) simulation technique. The values of the evaporation/condensation coefficient are estimated.