In plasma spraying, compared to other thermal spraying process variants, only a small part of the available energy is used to build up a coating. Another peculiarity of this process is the relatively strong oxidation of the sprayed metallic particles, caused by the high temperatures and turbulent flow of the plasma jet in combination with the ambient air. A promising solution for increasing energy efficiency is a solid shroud that surrounds the plasma jet and thus prevents air entrainments from mixing with the plasma gas. The primary goal of this study is to develop a numerical model to investigate the effect of an external fixed nozzle extension on the plasma jet as a shroud. To this end, the existing simulation models of the plasma jet from the previous works of the authors were extended to model a solid nozzle extension at the outlet of a three-arc plasma generator. Furthermore, the length and diameter of the nozzle extension were parametrized to investigate their effects on the plasma temperature and the turbulence of the flow. This model can be used to optimize the geometry of the nozzle extension based on experimental measurements to adapt it to the flow conditions of the plasma jet. The results revealed that the plasma temperature could be increased using the nozzle extension, thereby raising the energy efficiency to melt the particles in plasma spraying.