The high-intensity free-burning are is modeled using a computational domain including the are itself and the are cathode and anode. It is shown that the energy equation with the temperature, instead of the specific enthalpy, as the dependent variable has to be used in order to obtain physically reasonable heat fluxes from the plasma to the electrodes if a SIMPLE-like algorithm is employed in the modeling. New difficulty encountered in the numerical solution of the energy equation is discussed in some detail and has been overcome successfully by use of a 'pseudo-density' method and a deferred-correction discretization scheme. A more realistic boundary condition is adopted at the rear face of the anode plate for the solution of the potential equation in order to reveal the effect of electrical collection at the anode on the current density and temperature distributions within the anode plate. Special treatments at the plasma-electrode interfacers are also discussed and adopted ill the modeling.