Controlling the cooling rate experienced by a material during a manufacturing process is a challenge and a major issue. Industrial processing techniques are very diverse and may involve a whole range of cooling rates, which are sometimes extremely high for small and/or thin manufactured parts. For polymers, the cooling rate has consequences on both the microstructure and the time-dependent properties. The common cooling rates associated with conventional calorimetric measurements are generally limited to a few tens of degrees per minute. This work combines several calorimetric techniques (DSC, modulated-temperature DSC, stochastically-modulated DSC and Fast Scanning Calorimetry) to estimate the critical cooling rate required to melt-quench fast-crystallizing polyesters to their fully amorphous state, based on the example of a series of poly(alkylene trans-1,4-cyclohexanedicarboxylate) (PCHs) with a number of methylene groups in the main structure of the repeating unit nCH2 varying from 3 to 6. The even-numbered ones require faster cooling rates (about 3000 K s−1 for nCH2 = 4, between 500 and 1000 K s−1 for nCH2 = 6) compared to the odd-numbered ones (between 50 K min−1 and 100 K s−1 for nCH2 = 3, between 10 and 30 K min−1 for nCH2 = 5).