A solid material is placed near a heat source whose temperature and electrical potential remain constant. Heat transfer across the gap between the solid body and the heat source can take place via gap conductance or gap radiation (thus, there are two tests for each element type). Electrical current is conducted between the two closely adjacent surfaces forming the gap. Half of the electrical energy resulting from this conductance is released as heat and is distributed equally to the two adjacent surfaces. No Joule heating occurs in the model as a result of electrical conduction; therefore, electrical energy does not act as an internal heat source within the continuum elements. For simplicity we initiate a unidirectional heat flow and current in the solid by applying a higher temperature and electrical potential to the face farthest from the heat source. The steady-state temperatures and electrical potentials of the solid face closest to the heat source are verified with the analytical solution.