In contrast to the thermal unfolding of native proteins, very few studies of the thermally induced melting of amyloid fibrils have been reported to date due to the complex nature of these protein aggregates and the lack of theoretical formalisms to rationalize the data. In this work, we analyzed the thermal melting of the amyloid fibrils of the N47A mutant of the alpha-spectrin SH3 domain by differential scanning calorimetry (DSC). The thermal melting of the isolated fibrils occurred in single endothermic transitions, yielding the fully unfolded protein. The enthalpy and heat capacity changes of fibril melting were significantly lower than those of the unfolding of the native protein, indicating a lower density of interactions and a higher solvent-exposed surface area for the protein within the fibrils relative to the native state. In addition, these magnitudes did not change significantly between fibrils showing different morphology. The independence of the transitions with the scan rate and the observation of a considerable mass-action-like effect upon the melting temperatures indicated that the fibril melting is not separated significantly from equilibrium and could be considered in good approximation as a reversible process. A simple equilibrium model of polymerization coupled to monomer unfolding allowed us for the first time to interpret quantitatively the thermal melting of amyloid fibrils. The model captured very well the general features of the thermal behavior of amyloid fibrils and allowed us to estimate the partitioning of the energy of overall melting into the unfolding of monomers and fibril elongation. We conclude that with the use of appropriate models of analysis DSC has an extraordinary potential to analyze the thermodynamic determinants of amyloid fibril stability.