We report on a novel approach to determine the relationship between the corrugation and the thermal stability of epitaxial graphene grown on a strongly interacting substrate. According to our density functional theory calculations, the C single layer grown on Re(0001) is strongly corrugated, with a buckling of 1.6 Angstrom, yielding a simulated C 1s core level spectrum which is in excellent agreement with the experimental one. We found that corrugation is closely knit with the thermal stability of the C network: C-C bond breaking is favored in the strongly buckled regions of the moire´ cell, though it requires the presence of diffusing graphene layer vacancies.