Although melting of flexible macromolecules is an irreversible process, it was demonstrated recently with temperature-modulated calorimetry (TMC) that some of the overall melting may be reversible within a fraction of a kelvin. This was taken as evidence for incompletely melted molecules with a remaining molecular nucleus. The reversing heat capacity that characterizes this effect was observed to decrease with time. It is shown by new TMC experiments that this time effect is not induced by the temperature modulation, but is due to an inherent annealing process. It is also proven that it is not dependent on the type of calorimeter.