A new mathematical model for spheroidal droplet heating and evaporation is proposed. This model takes into account the effect of liquid finite thermal conductivity and is based on the previously obtained analytical solution for the vapour mass fraction at the droplet surface and a new correlation for the convective heat transfer coefficient incorporated into the numerical code. The heat transfer equation in the liquid phase is solved numerically using the finite-element heat transfer module of COMSOL Multiphysics. It is shown that the lifetime of spheroidal (prolate and oblate) droplets is shorter than that of spherical droplets of the same volume. The difference in the lifetimes of spheroidal and spherical droplets, predicted by the new model, is shown to increase with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. As in the case of stationary spherical droplets, the d2-law is shown to be valid for spheroidal droplets after the completion of the heat-up period. The predictions of this model agree with experimental observations. The duration of the heat-up period is shown to decrease with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. The maximal surface temperatures are predicted near the regions where the surface curvature is maximal. The aspect ratios are shown to be weak functions of time, in agreement with experimental observations. •A new mathematical model for spheroidal droplet heating and evaporation.•Effect of non-uniform surface temperature on droplet heating and evaporation.•The effect of liquid finite thermal conductivity is considered using COMSOL.•An analytical solution for the vapour mass fraction at the droplet surface is used.•A new correlation for the convective heat transfer coefficient is obtained and used.