The motion of the gliding DC electric arc under the effect of magnetic field is investigated. The temperature distribution in the inside and the outside of the moving arc is computed. The temperature distribution for the fixed-spot arc is also obtained. It appears that the gas relative velocity inside the arc gives rise to heat convection, which has an impact on the arc motion. A practical analytical solution is derived using magneto gas dynamic equations in order to investigate the heat transfer occurring in the arc and its vicinity, to determine its characteristics, and to estimate its velocity when it is exposed to external and electrode-induced magnetic fields. Two methods are suggested: one for the free-burning arc and the other for arc burning between close surrounding walls.