Metalloproteins make up a class of proteins that incorporate metal ions into their structures, enabling them to perform essential functions in biological systems, such as catalysis and electron transport. Azurin is one such metalloprotein with copper cofactor, having a β-barrel structure with exceptional thermal stability. The copper metal ion is coordinated at one end of the β-barrel structure, and there is a disulfide bond at the opposite end. In this study, we explore the effect of this disulfide bond in the high thermal stability of azurin by analyzing both the native S-S bonded and S-S nonbonded (S-S open) forms using temperature replica exchange molecular dynamics (REMD). Similar to experimental observations, we find a 35 K decrease in denaturation temperature for S-S open azurin compared to that of the native holo form (420 K). As observed in the case of native holo azurin, the unfolding process of the S-S open form also started with disruptions of the α-helix. The free energy surfaces of the unfolding process revealed that the denaturation event of the S-S open form progresses through different sets of conformational ensembles. Subsequently, we compared the stabilities of individual β-sheet strands of both the S-S bonded and the S-S nonbonded forms of azurin. Further, we examined the contacts between individual residues for the central structures from the free energy surfaces of the S-S nonbonded form. The microscopic origin of the lowering in the denaturation temperature is further supplemented by thermodynamic analysis.