A systematic study of the thermal properties of an artificial molecular formed by a single electron and two laterally coupled quantum rigs under external probes: magnetic and static electric fields was carried out. The eigen-states and eigen-values of the Hamiltonian under the framework of effective mass approximation were obtained numerically. By varying the separation between their centers, it was possible to establish the equilibrium length required for the formation of giant stable artificial molecular complex and its dissociation energy. These features were corroborated by studying the effects of the distance between centers of the rings, the magnetic and electric field on the entropy and heat capacity of the system. At low temperatures, the equilibrium condition of the two laterally coupled quantum rings artificial molecule is linked to the formation of a minimum value of the entropy and a peak in the heat capacity. The temperature’s rising modifies substantially these conditions.