We investigate the deformation of an infinitely long, circular cylindrical electric conductor carrying a uniform axial current, for the case when the electric conductivity of the coating is temperature dependent. This model conforms with the real situation for many of the existing modern dc cables with polyethylene coating. The distributions of temperature, magnetic field, stresses, and displacements in the cable are obtained and discussed under a thermal radiation condition at the boundary of the cable. In particular, it appears that there is a critical temperature for the ambient medium to the cable, above which no solution for the steady heat problem can exist and the thermal equilibrium of the cable is no longer fulfilled. A formula for the calculation of this critical value is given, which may turn out to be of practical importance for a reliable design of the cable. The obtained results also show that the electric conductivity of the coating strictly decreases as one moves from the core to the boundary of the cable in conformity with the behavior of temperature. Some numerical results are presented.