An idealy structured solid dielectric material formally has zero electrical conductivity (later on conductivity) and does carry an electric current. However real materials, used as solid dielectrics, have relatively low, but still finite conductivity, which, generally, increases with increasing temperature. Conductivity of solid dielectrics versus temperature corresponds to the exponential function, which by sight corresponds to the formula for Boltzmann distribution of microparticles in energy levels. In case there is a constant difference of potentials on the dielectric layer surfaces an electric current flows through this layer, causing Joule heat, which, under steady-state conditions, should be removed to the external environment. Inadequate heat removal rate leads to increasing temperature of dielectric, its increasing conductivity and electric current density, thereby increasing the volumetric capacity of the energy release in the dielectric, i.e. a positive feedback effect occurs to cause a quick growth of temperature culminating in the heat destruction of dielectric material (melting, carbonization). This process is called heat breakdown of the dielectric, apart from the electric breakdown. Investigation of conditions for emerging dielectric heat breakdown is associated with the analysis of rather complicated nonlinear mathematical model that permits an analytical solution in a closed form only for a flat or cylindrical dielectric layer through simplifying a dependence of dielectric conductivity on the temperature. In this paper, the model is assigned to a variational form that contains a functional. An analysis of stationary points of this functional allows us to find a combination of parameters that determine the ultimate state of the dielectric layer before the heat breakdown, in particular so-called breakdown voltage.