A two-temperature (2-T) model for tungsten inert gas (TIG) welding process is developed to investigate the arc phenomena of the pure argon and helium plasmas. The model considers the energy conservations of the heavy particles and the electrons separately. Compared with the 1-T model, the 2-T model obtains the plasma shapes more similar to the arc appearances. Furthermore, the heavy particle temperature of the 2-T model shows good agreement with the experimental results. For a pure helium arc, the electron temperature is much higher than the heavy particle temperature, whereas both temperatures are almost identical for a pure argon arc. Thermal non-equilibrium of a pure helium arc is discussed in terms of the energy exchange between heavy particles and electrons. It is found that ions and atoms of a pure helium arc cannot exchange their energy sufficiently with electrons because the plasma has a small number of electrons and consequently the collision rate between plasma species is relatively low. The simulation results show that when a welding current is lower, thermal non-equilibrium of an arc plasma is stronger. In a low welding current condition, not only the pure helium arc but also the pure argon arc shows thermal non-equilibrium.