Abstract: In this paper a plane heat conduction problem with variable coefficients of heat conductivity K(T) is analysed with given electric power supplied to the plasma arc. The governing equation for unknown temperature distribution is a nonlinear one with a δ function as its nonhomogeneous term. To make the problem attractable by the method of separation of variables, a set of transformation of governing equation is introduced. An explicit simple formula is found for the efficiency of the furnace η, η depends linearly on r₀, the nondimensional distance between the arc and surface of melted material, as well as on another nondimensional quantity Q, we describe the above in detail in this paper. This relationship holds for r₀<0.4 and gives a good guidance for the design of furnace.