This study presents an analysis of a three-dimensional unsteady two-temperature simulation of atmospheric pressure direct current electric arc inside a commercial cascaded-anode plasma spray torch; it coupled the arc model with the torch electrodes and used an open-source computational fluid dynamics software (code_saturne). The previously published models of plasma spray torch either deal with conventional plasma torches or assume local thermodynamic equilibrium in cascaded-anode plasma torches. The paper presents the computation of the two-temperature argon plasma properties, compares two enthalpy formulations that differ in association of the ionization part of enthalpy and finally demonstrates the influence of the radiation heat loss data by comparingthe results for two different literature sources. It is the first to compare different enthalpy formulations in the context of plasma torch and discuss the differences in terms of the enthalpy gains and losses. It also explains why an unphysical simulation artifact of electron temperature lower than the heavy species temperature can occur in simulated plasma flow. The solution, then, consists in associating the ionization part of enthalpy to electrons and selecting the appropriate source of the data of radiation heat loss. However, negligible thermal non-equilibrium persists even in the hot core of electric arc, which ensures that the heavy species are heated up by collisions with electrons. The flexibility of the open-source software allows all the necessary modifications and adjustments to achieve satisfactory simulation results. Thus, the paper could be considered as a manual for development of a plasma spray torch model.