The article presents an electrical model of a resistance furnace with two electrodes encompassing the generation of Joule heat. The characteristic feature of this model was the consideration of contact resistance between the electrodes and the slag. A series of analyses were conducted based on this model. Firstly, the impact of contact resistance on current flow and Joule heat generation in the furnace was assessed, demonstrating its significant importance. A separate group of analyses focused on the spatial configuration of the furnace and its interaction with the aforementioned phenomena. The impact of symmetric and asymmetric electrodes immersion was analysed. In addition to the impact on current flow, the study also demonstrated the influence on the natural convection mechanism described by the proposed measures of the spatial non-uniformity of heat generation. The research showed that symmetric electrode immersion allows for the generation of more heat in the system at a constant voltage. Asymmetric electrodes immersion causes an increase in the non-uniformity of heat generation, which translates into a higher intensity of natural convection.