One of the key aspects of particle behavior in the plasma jet is the stochastic nature of the injection process. Particles are injected into the plasma jet with a certain variation in initial velocity which, along with their size distribution, determines the form of the layer structure and the degree of melting. The aim of this work is to model the influence of the initial spray parameters on the main characteristics of spray particles, such as temperature, velocity, and degree of melting, during impact with the substrate. A one-dimensional heat conduction equation that accounts for phase transitions is solved numerically for spherical particle shapes. The dynamic particle problem is also solved and an integral criterion for the coating model is obtained. Paper includes a German-language abstract.