The loss of the insulin-producing beta-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 beta 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 mu s per system studied, we show that sequences sample alpha-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 a-helix is known to be an important transient stage in the formation of oligomers. In the C-terminal, the amyloidogenic region of hIAPP, beta-strands are seen for residues 17-26 and 30-35. On the contrary, no significant beta-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 a-helical structure but rather play a significant role in stabilizing the amyloidogenic region available for the fibrillation.