A methodical 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 were carried out. The corresponding Schrödinger equation for these two coupled donors system was numerically solved by using the finite element method within the effective mass approximation. The effects of the donor angular and radial positions on the entropy, heat capacity and internal energy were analysed. 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, applying an intense laser or an external electric field can reduce this property in real time.