A three-dimensional model of a dc plasma torch with a rod-type cathode at atmospheric pressure has been developed in order to study a magnetically rotating arc in argon. The interplay between the arc and the plasma flow is described by means of magnetohydrodynamic equations in combination with a K-turbulence model. The simulation study is performed in terms of a two-temperature description (different electron and heavy particle temperatures). In the absence of magnetic field, the electron and heavy particle temperatures are nearly identical in the arc core, while near the walls, in the arc fringes and in the plume there are significant differences. With the magnetic field present, deviations from LTE appear even in the arc core and electron and heavy particle temperature differ there by about 10% thus emphasizing the need for a two-temperature treatment. The high temperature plasma region constrains in the axial and expands in the radial direction. The gas temperature gets lower by 2000 K in the arc core. In a moderately strong magnetic field, the magnetically driven plasma rotation is resolved and deviations from the axial symmetry are observed. Results for plasma and flow parameters are obtained and discussed.