In this paper a two‐temperature model (Te ≫Th) is applied to a free‐burning, high‐intensity, atmospheric pressure argon arc. With appropriate boundary conditions and nonequilibrium thermodynamic and transport properties, solutions of the conservation equations are obtained for the entire arc, except for the electrode sheath regions. Significant temperature discrepancies between electrons and heavy particles are found in the arc fringes. The elevated electron temperatures in the arc fringes lead to a rearrangement of the current density distribution which, in turn, has some effect on the temperature as well as on the velocity field in the arc core. Comparisons of the results of this study with spectrometric temperature measurements show better agreement than with results based on a one‐temperature model.