In numerical analysis of an arc plasma, the current density distribution and temperature distribution along the electrode surface are the most important boundary conditions, and a more accurate analysis can be achieved with a correct description of them. It was found that a distributed temperature condition taken from measured data makes isothermal contours broaden. The current density on the electrode surface was assumed to have a Gaussian distribution and its distribution parameters could be calculated for various electrode vertex angles. Analytically calculated distribution parameters helped the calculated temperature contours of the arc plasma to conform fairly well with experimental data.