Aliphatic/aromatic thermoplastic polyesters are a very interesting family of polymers with many applications. Poly(alkylene 2,5-furandicarboxylate)s (PAF)s are the biobased alternatives to poly(alkylene terephthalate)s and are expected to play a key role in bioeconomy. The most important PAFs are poly(ethylene 2,5-furandicarboxylate) (PEF), poly(propylene 2,5furandicarboxylate) (PPF), and poly(butylene 2,5-furandicarboxylate) (PBF), which crystallize slowly. PBF shows a typical PAF thermal behavior but a little faster crystallization compared to that of PPF and PEF. PBF was used in this work as a model material to understand the key parameters of the solidification of PAFs during processing. A detailed study of the kinetics of isothermal and dynamic melt and cold crystallization of PBF at very slow and moderate cooling and heating rates (0.1−20 °C/min) was carried out. Multiple melting was also analyzed. The equilibrium melting temperature was determined (T m o = 196.4 °C). The activation energy of non-isothermal crystallization from the melt decreased with increasing the cooling rate, in accordance with an increasing crystallization rate with supercooling. The cold-crystallization rate increased with increasing the difference between the cold-crystallization temperature (T cc ) and the glass transition temperature (T g ), which in turn increased with the heating rate. Several theoretical models were elaborated for the treatment of the crystallization data. Polarized optical microscopy revealed the formation of ring-banded spherulites at elevated temperatures (T c )s.