The Tool-Narayanaswamy-Moynihan model (TNM) is widely accepted in order to describe the enthalpy recovery mechanism of polymers. However, some problems have been found in quantitative analysis as far as the parameters of the model are concerned. In particular, in several studies, the values of the Kauzmann temperature have been obtained 150 K or more below the glass transition, whereas other works have provided values of the activation energy of the relaxation times at the glass transition that are inconsistent with viscoelastic or dielectric measurements. In this paper, we analyze differential scanning calorimetry experiments in a low molecular weight PMMA sample in terms of a modified TNM model, where the adjustable parameters only provide the behaviour of the out-of-equilibrium relaxation times. The temperature dependence of the equilibrium relaxation times is instead set at the values determined by the shear viscosity data of the sample. A good agreement between theory and experiments is obtained suggesting that the difficulties quoted above could actually depend on the TNM handling of the nonlinear effects.