Within the framework of a scientific collaboration between the University of Limoges, France and the State University of New York, Stony Brook, USA, a joint work has been conducted on microstructure development and properties of plasma-sprayed molybdenum coatings. This first part of the work is devoted to the study of the effect of substrate nature and temperature on splat cooling, solidification and crystalline structure. They were investigated by means of a heat transfer model in the splat and the substrate, and the observation of splats by a scanning electron microscope and an atomic force microscope. The model takes into account melt undercooling, nucleation and crystal growth, as also a possible melting and re-solidification of the substrate. It has the capability to predict the grain size distribution under assumptions that the quality of contact between the splat and the underlying layer is uniform, nucleation takes place only on the substrate surface, crystal grains grow perpendicular to the substrate surface and no grain coalescence occurs during crystal growth.