A plasma-sprayed coating is built up by the layering of individual splats. The latter are formed by spreading and solidification of molten particles sprayed onto a solid substrate. The coating properties depend on its microstructure and the quality of contact between the splats and the underlying layer and between the piled-up splats. This work deals with a 1D model of heat transfer between plasma-sprayed alumina splat and smooth substrate. The model is based on heat diffusion in the solidifying splat and substrate and includes undercooling phenomenon, heterogeneous nucleation and crystal growth kinetics. It assumes that splat spreading and solidification are two independent processes. The model predicts splat cooling and solidification taking into account, as far as possible, the in-flight particle properties drawn from the literature in order to study their effect on splat thermal history. The effect of the quality of contact between the splats as well as the already-deposited and solidified layer thickness on the grain size distribution and front solidification velocity is investigated.