Renewable, biodegradable polymers, such as aliphatic polyesters, based on sustainable sources have attracted considerable interest as alternatives to petroleum-based polymers. One limiting factor in the development of aliphatic polyesters as replacements for these materials has been their relatively low glass transition temperatures (T_g). For example, commercially available poly(lactic acid) has a T_g of approximately 60 °C. Epoxide/anhydride copolymerizations offer an alternative to the ring-opening polymerization of lactones for the synthesis of aliphatic polyesters and allow for tuning of polymer properties through two distinct monomer sets. We synthesized six partially or fully renewable tricyclic anhydrides and copolymerized them with propylene oxide (PO) and cyclohexene oxide (CHO). By varying both the epoxide and the anhydride, we were able to tune the T_g of the resulting polymers over a nearly 120 °C range from 66 °C to an exceptionally high 184 °C. Polymers produced with PO had a lower range of T_g values (66–108 °C) and higher molecular weights up to 32.2 kDa, while those produced with CHO had higher T_g values (124–184 °C) and lower molecular weights, showing the profound influence of both monomer sets. To the best of our knowledge, these are the highest T_g values reported for entirely aliphatic polyesters.