In this work, a mathematical model of the thermo-temporal evolution of a cluster in the melt of a heat-resistant nickel alloy ZhS6U is constructed. An initial-boundary value problem with a moving boundary is formulated, for the solution of which numerical modeling is used by the particle trajectory method, and a number of classical physical theories are used to describe evolutionary processes. To check the accuracy of the model, a physical experiment is involved in constructing polytherms and isotherms of the electrical resistance of the alloy under consideration. It has been confirmed that the Brownian diffusion model and Drude's theory of conductivity are applicable to describe both the temporal and temperature evolution of a cluster. The approach to modeling based on "hard balls" also justified itself. According to the simulation results, in the time range from 1690 to 1752 K, the number of particles in the cluster varies from 5000 to 2000, the average dynamic viscosity of the cluster varies from 3 to 2 * 1010 Pa * s, however, it is assumed that the central part is much denser than periphery. The cluster radius varies from 24 to 18 Å, and the radius of the free zone around the cluster varies from 56 to 43 Å. The directions of further development of the model are determined.