The electrical method of measuring the hardness of an electrically conducting material proposed by Haug et al. is based on the classical electrical contact theory. This theory assumes a thermal equilibrium in the system. However, in some conditions and for some materials, this assumption is not satisfied, particularly for high temperatures. To specify the domain of application of this method, the authors study the equilibrium stability. The case of tungsten is considered in detail: in this case, it is shown that the assumption of thermal equilibrium can be verified. In the general case, it is shown that this equilibrium is conditioned only by the electrical (resistivity), thermal (conductivity) and mechanical (hardness) characteristics of the material. This allows one to define a criterion of the system stability and so of the proposed application of the measurement method.