The enthalpy recovery mechanism of polymers is usually described in terms of the Tool-Narayanaswamy-Moynihan model (TNM). Even if it is able to qualitatively reproduce all the peculiar features of the aging process, clear discrepancies have been found in quantitative analysis. In this work, differential scanning calorimetry experiments are performed in two different polymers, and data are used in order to compare the predictions of a recently developed configurational approach with possible extensions of the TNM model. All the approaches add a free parameter with respect to the original TNM model. In this study we have found that appreciable improvements between experimental and calculated DSC traces can be observed if the configurational entropy approach is adopted. Furthermore, the long-term annealing experiments performed in one of the polymers clearly support the basic hypothesis of the entropic approach concerning the limit state of the structural relaxation.