The paper considers a mathematical model describing the time evolution of spin states and magnetic properties of a nanomaterial. We present the two variants of nanosystems simulations results. In the first variant, cobalt with a structure close to the hexagonal close-packed crystal lattice was considered. In the second case, the volume of the same size cobalt nanofilm formed in the previously obtained computational experiment of multilayer niobium-cobalt nanocomposite deposition was investigated. For both simulations, it is obtained that, after pre-correction and significant jumps in the initial time moments, the change in spin temperature occurs in a small range of values near the average value. The system with a real structure has a less stable behavior of the spin temperature and a larger scatter of instantaneous values. For all cases of calculations for cobalt, the ferromagnetic character of the behavior is preserved. Defects in the structure and the local arrangement of the atoms can cause a deterioration of the magnetic macroscopic parameters, such as a decrease in the magnetization modulus.