We apprehend heat transfer from the body at higher temperature to the body at lower temperature at heat exchange as a fundamental property of environment. But as it is known the direction of a thermodynamical process passing is determined by entropy, and in the case of nonequilibrium heat exchange it may lead to heat transfer in unusual direction. In the thermodynamical system in which a nonmonotonous dependence exists between entropy and energy, for example, when a molecular construction of one of the bodies has a limited number of a quantum state, a spontaneous heat transfer from the body at lower temperature to the body at higher temperature is possible. A theoretical possibility of the inversion of a heat flow direction is shown in the paper. The experiment in the system at limited number of quantum states allowed certifying a dominant importance of entropy when defining the direction of the thermodynamic processes passing as well as the possibility of a practical realization of a heat flow inversion. Keywords: entropy, heat flow direction, spontaneous heat transfer from the body at low temperature to the body at high temperature, magnetic entropy, quantum states of the body.