This paper presents a I-D heat transfer model which predicts the solidification and cooling of a plasma-sprayed alumina splat after the flattening process is completed. A heterogeneous nucleation process taking place on the substrate surface was assumed. The density and average size of the formed nuclei were determined from the integration of the nucleation rate calculated from the classical kinetic theory for nucleation. This rate depends on the activation energy required for nucleation which takes into account the effect of the surface via a wetting angle between the growing nucleus and the catalytic surface. This contact angle was estimated from the comparison of the computed grain density with the density observed on splat surface using an atomic force microscope. When 67 % of the splat surface in contact with the substrate are covered by grains, a planar solidification front was assumed to move through the melt. The theoretical model accounted also for the selection of the crystalline phase. Calculations were performed for various substrate materials at different initial temperatures. Results are expressed in terms of nucleation temperature, nucleation rate, density and grain size distribution.