The boundary conditions, at the walls for the electric potential, the electron energy equation, and the energy equation for heavy particles (ions and neutrals), for two-temperature thermal arc models are presented. In these boundary conditions, the plasma sheath formed at the wall is viewed as the interface between the plasma and the wall. Two cases are considered: cold walls with no thermionic electron emission and wall erosion and hot walls with thermionic electron emission. The hot walls are assumed to be made from refractory metals so that the erosion of the wall is small and can be neglected. The boundary conditions allow for the calculation of the heat flux from the plasma to the walls. In the case of hot electrodes, this allows for the calculation of the thermionic electron current that makes the model of electrode–plasma interaction self-consistent. The obtained boundary conditions are applied to a zero-dimensional model of the cathode spot, the anode attachment, and nozzle floating walls. It is demonstrated that in the case of a thermionic cathode, a virtual cathode can be formed if the cathode current density (at a given surface temperature of the cathode) is sufficiently small. It is also shown that using these boundary conditions in modeling of high-pressure plasma cutting arcs leads to much larger heat fluxes to the wall and significantly cooler arcs, compared to models that ignore the sheath at the wall.