This paper presents the quasi-stationary Stefan problem in symmetric electrical contacts.The method of the solution can be obtained from the suggestion that the identity of equipotential and isothermal surfaces in contacts, which is correct for stationary fields in linear case, keeps safe for non-linear case as well. The idea is,transform the system of problem which is given in cylindrical coordinates into ellipsoidal coordinates.The analytical solution of stationary Stefan problem is found. Based on that decision was constructed the temperature profile to the approximate solution of heat problem with Joule heating in ellipsoidal coordinates. Keywords: quasi-stationary model, Stefan problem, integral method.