Polyester block polymers containing polylactide have garnered significant attention as renewable, degradable alternatives to traditional elastomers. However, the low glass transition of the PLA blocks limits the upper-use temperatures of the resulting elastomers. To improve the thermal performance, we explore a series of multiblock polyesters composed of poly(e-decalactone) (PDL) and poly(cyclohexene phthalate) (PCHPE). These materials are prepared using switchable polymerization catalysis followed by chain extension. The strategy involves (i) alternating ring-opening copolymerization (ROCOP) of cydohexene oxide and phthalic anhydride, (ii) epsilon-decalactone ring-opening polymerization (ROP), and (iii) diisocyanate coupling of the telechelic triblocks to increase molar mass. The resulting multiblock polyesters are amorphous, and the blocks are phase separated; glass transition temperatures are, similar to-45 and 100 degrees C. They show thermal resistance to mass loss with T-d5% similar to 285 degrees C and higher upper use temperatures compared to alternative aliphatic polyesters. The nanoscale phase behavior and correlated mechanical properties are highly sensitive to the block composition. The sample containing PCHPE = 26 wt % behaves as a thermoplastic elastomer with high elongation at break (epsilon(b) > 2450%), moderate tensile strength (sigma(b) = 12 MPa), and low residual strain (epsilon(r) similar to 4%). It shows elastomeric behavior from -20 to 100 degrees C and has a processing temperature range of 170 degrees C. At higher PCHPE content (59 wt %), the material has shape memory character with high strain fixation (250%) and recovery (96%) over multiple (25) recovery cycles. The multiblock polyesters are straightforward to prepare, and the methods presented here can be extended to produce a wide range of new materials using a other epoxides, anhydrides, and lactones. This first report on the thermal and mechanical properties highlights the significant potential for this class of polyesters as elastomers, rigid plastics, and shape memory materials.