Obtaining uniform penetration on welding groove faces is one urgent problem in oscillation arc narrow gap welding; however, the heat flux distribution on the groove face under the deflected welding arc is difficult to investigate by the experimental method. In this article, a unified three-dimensional model is developed to study the heat flux distribution on groove faces. The model includes the electrode, welding arc, workpiece, and their coupling. The plasma arc profile, heat flux characteristics, and weld pool formation were simulated. Based on the simulation results, the following conclusions were contained. The deflecting degree of the welding arc axis is increased with the increasing of extra magnetic-field intensity, and this leads to the change of the distribution of conduction heat flux and electric heat flux. At the groove bottom, both heat fluxes move to one side, and their distribution shape changes from circular to elliptical. At the sidewall, the distribution shape of conduction heat flux is triangular, and that of electrical heat flux is elliptical. The maximum value of heat flux density decreased, and the affected area was increased with the associate of the extra magnetic field. The simulation welding bead was in agreement with the experimental result.