The growing ecological awareness of society created the tendency to replace petrochemically based materials with alternative energy carriers and renewable raw materials. One of the most requested groups of polymer materials with significant technological importance is thermoplastic elastomers (TPE). They combine the properties of elastomers such as flexibility with the typical properties of thermoplastics, like easy processing. Herein, one compares the influence of rigid segments on the properties of copoly(ester-ether). Thermoplastic polyesters based on bio-1,6-hexanediol and terephthalic (T), furanic (F), and napthalate (N) diesters, i.e., PHT, PHF, and PHN, were obtained employing melt polycondensation. Additionally, to grant elastic properties of polyesters, systems containing 50 wt.% of bio-based polyTHF®1000 (pTHF) with a molecular mass of 1000 g/mol, have been prepared. The composition and chemical structure have been determined by 1H nuclear magnetic resonance (NMR) and Fourier transformed infrared spectroscopy (FTIR) analyses. The temperatures corresponding to phase transition changes were characterized by differential scanning calorimetry (DSC) and dynamic mechanical thermal analysis (DMTA) analyses. The crystalline structure was examined by X-ray diffraction (XRD) analysis. Additionally, the influence of pTHF–rich segment on the tensile properties, water absorption, as well as thermal and thermo-oxidative stability, has been analyzed. It was found that incorporation of soft phase allows creation of thermoplastic elastomers with tensile characteristics comparable to the commercially available ones, by means of elongation at break higher than 500%, low values of tensile modulus, without exhibiting yield point.