A detailed understanding of anode heat transfer is important for the optimization of arc processing technology. In this paper, a two-temperature chemical non-equilibrium model considering the collisionless space charge sheath is developed to investigate the anode heat transfer of nitrogen free-burning arc. The temperature, total heat flux and different heat flux components are analyzed in detail under different arc currents and anode materials. It is found that the arc current can affect the parameter distributions of anode region by changing plasma characteristics in arc column. As the arc current increases from 100 A to 200 A, the total anode heat flux increases, however, the maximum electron condensation heat flux decreases due to the arc expansion. The anode materials have a significant effect on the temperature and heat flux distributions in the anode region. The total heat flux on thoriated tungsten anode is lower than that on copper anode, while the maximum temperature is higher. The power transferred to thoriated tungsten anode, ranked in descending order, is heat flux from heavy-species, electron condensation heat, heat flux from electrons and ion recombination heat. However, the electron condensation heat makes the largest contribution for power transferred to copper anode.