On the basis of a simplified theoretical model an analysis is given of the stationary state of a cylindrical column of fully ionized high-pressure plasma, which is heated by an axial current and cooled by heat conduction in the radial direction across the self-magnetic field of the current. The radial distributions of current, magnetic field, temperature, pressure, and density are calculated and discussed. The power needed to maintain a stationary state at very high temperatures is found to be moderate. The relative importance of radiation losses is considered and found to be small in a certain range of parameters.