Crystallization of poly(butylene succinate) (PBS) at 100 degrees C, about 30 K below the equilibrium melting temperature, allowed the preparation of crystals, which were analyzed regarding their zero-entropy-production melting temperature. Irreversible melting occurs in a rather narrow temperature window of only around 8 K, between 101 and 109 degrees C, revealing a narrow distribution of the thickness of isothermally formed lamellae and a rather low thickening/stabilization factor of less than 1.4. Quasi-isothermal temperature-modulated differential scanning calorimetry suggests significant reversible melting and crystallization during and after crystallization, proving the existence of a large fraction of crystalline phase being at the stability limit at the crystallization temperature. Heating of crystals formed at 100 degrees C to above their zero-entropy-production melting temperature, followed by isothermal annealing, permitted the analysis of the kinetics of irreversible melting, yielding superheating-dependent rate constants of the order of magnitude of 102 s(-1) 5-10 K above the zero-entropy-production melting temperature. The advanced analysis of the melting behavior of polymer crystals isothermally grown at low melt supercooling allows one to draw conclusions about their (inherently) low thermodynamic stability.