A two-dimensional model of the non-equilibrium unipolar discharge occurring in the plasma-sheath boundary region of a transferred-arc was developed. This model was used to study the current transfer to the nozzle (1 mm diameter) of a 30 A arc cutting torch operated with oxygen. The energy balance and chemistry processes in the discharge were described by using a kinetic block of 45 elementary reactions and processes with the participation of 13 species including electronically excited particles. The nonlocal transport of electrons was accounted for into the fluid model. The dependence of the ion mobility with the electric field was also considered. Basic discharge properties were described. It has been found that a large part (similar to 80%) of the total electric power (1700 mW) delivered in the bulk of the sheath region is spent in heating the positive ions and further dissipated through collisions with the neutral particles. The results also showed that the electron energy loss in inelastic collisions represents only similar to 25% of the electron power and that about 63% of the power spent on gas heating is produced by the ion-molecule reaction, the electron-ion and ion-ion recombination reactions, and by the electron attachment. The rest of the power converted into heat is contributed by dissociation by electron-impact, dissociative ionization and quenching of O(D-1). Some fast gas heating channels which are expected to play a key role in the double-arcing phenomena in oxygen gas were also identified.