The enzymatic synthesis of polyesters in solventless systems is an environmentally friendly and sustainable method for synthetizing bio-derived materials. Despite the greenness of the technique, in most cases only short oligoesters are obtained, with limited practical applications or requiring further chemical processing for their elongation. In this work, we present a catalyst-free thermal upgrade of enzymatically synthesized oligoesters. Different aliphatic and aromatic oligoesters were synthesized using immobilized Candida antarctica lipase B (iCaLB) as the catalyst (70 °C, 24 h) yielding poly(1,4-butylene adipate) (PBA, Mw = 2200), poly(1,4-butylene isophthalate) (PBI, Mw = 1000), poly(1,4-butylene 2,5-furandicarboxylate) (PBF, Mw = 600), and poly(1,4-butylene 2,4-pyridinedicarboxylate) (PBP, Mw = 1000). These polyesters were successfully thermally treated to obtain an increase in Mw of 8.5, 2.6, 3.3, and 2.7 folds, respectively. This investigation focused on the most successful upgrade, poly(1,4-butylene adipate), then discussed the possible effect of di-ester monomers as compared to di-acids in the thermally driven polycondensation. The herein-described two-step synthesis method represents a practical and cost-effective way to synthesize higher-molecular-weight polymers without the use of toxic metal catalysts such as titanium(IV) tert-butoxide, tin(II) 2-ethylhexanoate, and in particular, antimony(IV) oxide. At the same time, the method allows for the extension of the number of reuses of the biocatalyst by preventing its exposure to extreme denaturating conditions.