At present, metal hydrides are considered highly promising materials for phonon-mediated superconductors, that exhibit high values of the critical temperature. In the present study, the superconducting properties of the compressed selenium hydride in its simplest form (HSe) are analyzed, toward quantitative characterization of this phase. By using the state-of-art Migdal-Eliashberg formalism, it is shown that the critical temperature in this material is relatively high ($T_{c}$=42.65 K) and surpass the level of magnesium diboride superconductor, assuming that the Coulomb pseudopotential takes value of $0.1$. Moreover, the employed theoretical model allows us to characterize other pivotal thermodynamic properties such as the superconducting band gap, the free energy, the specific heat and the critical magnetic field. In what follows, it is shown that the characteristic thermodynamic ratios for the aforementioned parameters differ from the predictions of the Bardeen-Cooper-Schrieffer theory. As a result, we argue that strong-coupling and retardation effects play important role in the discussed superconducting state, which cannot be described within the weak-coupling regime.
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