The spatial distribution of the electrothermal field within molten salt electrolytic cells significantly influences the efficiency of the electrolysis process, the quality of the end products, and the overall stability of the system. Enhancing the design of chloride electrolysis cells can lead to marked improvements in both process efficiency and system stability, thereby yielding increased economic benefits. This study introduces a design for a chloride electrolysis cell and examines the thermal budget under elevated electrical current intensities across 16 electrode pairs. It further analyzes the degree to which various parameters affect thermal equilibrium. The findings indicate that the electrolytic cell maintains a small thermal budget discrepancy at a current intensity of 124 kA and is less than 5%, with substantial heat dissipation observed at the surface of the top area of anode exposure and considerable energy consumption at both the anode and the electrolyte. Dimensionless treatment of the different parameterized simulation results has been conducted to develop a nondimensional equation, describing the thermal equilibrium conditions within the electrolytic cell. This foundational work paves the way for further investigations into the interactions between the electrothermal field and other physical fields, as well as for the optimization of the electrolytic cell's geometry and design.