New solutions of the heat conduction equation inside a spherical droplet are obtained. The droplet is assumed to be heated by convection and radiation from the surrounding hot gas-a situation typical in many engineering applications. Initial droplet evaporation and the effects of time dependent gas temperature and convection heat transfer coefficient are taken into account. In the cases of constant, and almost constant convection heat transfer coefficients, the explicit formulae for time dependent radial distribution of temperature inside droplets are obtained. In the case of arbitrary convection heat transfer coefficient, the differential equations are reduced to the Volterra integral equation of the second kind. A numerical scheme for the solution of this equation is suggested. The solution for constant convection heat transfer coefficient is applied to a typical problem of fuel droplet heating in a diesel engine. It is shown that finite thermal conductivity of fuel droplets and the effects of radiation need to be taken into account when modelling droplet heating in diesel engines. (C) 2004 Elsevier Ltd. All rights reserved.