A systematic study of the thermal properties of a hydrogen molecular ion strongly confined in a flat semiconductor quantum ring under external probes: intense laser-field radiation and static electric fields was carried out. The corresponding Schrödinger equation for these two coupled donors system was numerically solved by using finite element method within the effective mass approximation. The effects of the donors angular and radial positions on the entropy, heat capacity and internal energy were analyzed. Results show that the entropy of the system is maintained low as long as the molecule preserves its integrity but if the molecule is fragmented, the randomness of the system is substantially increased. Nevertheless, this property can be reduced in real time by applying an intense laser field or an external electric field