This article uses mathematical mathematical models of tasks by Stefan and Stefan-Schwarz describing the technologies of IMSCHA "Acad. A. Balevski ". Described are processes for solidifying a drop (droplet) over a surface of a metal substrate. Processes of solidifying of metal melts in the form of spheres having a radius of 50 nm are described. The temperature fields of the open thermodynamic system drop / substrate system are presented. The influence of the change of specific parameters from the hardening process is represented by the type of the temperature field of the OTS.