ones you are at the vicinity of the crystallization temperature, first the polymer is already surpassed its Tg, this means that it is at least in a rubber-like state. When you approch the Tc means the material softeness more and approaches the melting or free flowing. On the other hand, sometimes this done to increase the crystal density and perfection, it called annealing. So, what is happening depends on what you are intending to study. At USTHB, you have many well recognized Professors in polymer science such as Prof. Djaedoun and Prof. Mouzali (who was the chairman in my master thesis jury). Regards
You say that you have semi-crystalline polymer, it can safely be considered that your polymer will have amorphous phase also. At crystallization temperature, this amorphous phase will also crystallize. You may get an exothermic peak at this temperature in DSC experiment.