The loss of the insulin-producing β-cells in the pancreatic islets of Langerhans, responsible for type-II diabetes, is associated with islet amyloid deposits. The main component of these deposits is the amyloid fibrils formed by the 37-residue human islet amyloid polypeptide (hIAPP also known as amylin). Although the fibrils are well characterized by cross β structure, the structure of the transient oligomers formed in the early stage of aggregation remains elusive. In this study, we apply the Hamiltonian-temperature replica exchange molecular dynamics to characterize the structure and thermodynamics of a full-length hIAPP dimer in both the presence and the absence of the Cys2-Cys7 disulfide bond. We compare these results with those obtained on the monomeric and dimeric forms of rat IAPP (rIAPP) with a disulfide bridge which differ from the hIAPP by 6 amino acids in the C-terminal region, but it is unable to form fibrils. Using a coarse-grained protein force field (OPEP-the Optimized Potential for Efficient peptide structure Prediction) running for a total of 10-28 μs per system studied, we show that sequences sample R-helical structure in the N-terminal region but that the length of this secondary element is shorter and less stable for the chains without the disulfide bridge (residues 5-16 for hIAPP with the bridge vs 10-16 for hIAPP without the bridge). This R-helix is known to be an important transient stage in the formation of oligomers. In the C-terminal, the amyloidogenic region of hIAPP, β-strands are seen for residues 17-26 and 30-35. On the contrary, no significant β-sheet content in the C-terminal is observed for either the monomeric or the dimeric rIAPP. These numerical results are fully consistent with recent experimental findings that the N-terminal residues are not part of the fibril by forming R-helical structure but rather play a significant role in stabilizing the amyloidogenic region available for the fibrillation.