In the field of aliphatic polyesters there is a great interest in building novel macromolecular structures that may effectively feature the required properties for specific applications. For this reason, it is extremely important to understand the correlations between chemical structure and final performance. Monomers based on the 1,4-cyclohexylene unit are interesting as they are potentially bio-based and rigid enough to improve glass transition and melting temperatures. The present paper describes the preparation of samples of poly(1,4-cyclohexylenedimethylene adipate), characterized by different cis/trans isomeric ratio of the cyclic units, the analysis of their thermal properties and the comparison with the properties of similar polymers such as poly(butylene adipate), poly(butylene-1,4-cyclohexanedicarboxylate) and poly(1,4-cyclohexylenedimethylene-1,4-cyclohexanedicarboxylate). The effect of the rigidity and of the stereochemistry of the 1,4-cyclohexylene unit on the thermal properties was analysed. Such an effect reaches its maximum level when the cyclic-containing monomers are the diacid or the diester and when the trans isomers predominate. Starting from such a result, the combination of specific cyclic building blocks with the correct cis/trans ratio makes it possible to build macromolecular structures with the required final properties.