A composition and a process for straightening hair are disclosed. The process includes coating keratin fibers with a composition comprising a thermally-activated agent and contacting the coated keratin fibers with a heating device at a temperature of at least 185°C for sufficient time to modify the keratin fibers. The thermally-activated agent comprises a heterocyclic compound containing two heteroatoms selected from nitrogen and oxygen in a 5 or 6-membered ring, such as a cyclic alkylene carbonate.