Producing polyesters with high molecular weight (Mn) through ring‐opening copolymerization (ROCOP) of epoxides with cyclic anhydrides remains a major challenge. Herein, we communicate a metal‐free, highly active, and high thermoresistance system for the ROCOP of epoxides with cyclic anhydrides to prepare polyesters (13 examples). The organoboron catalysts can endure a reaction temperature as high as 180 °C for the ROCOP of cyclohexane oxide (CHO) with phthalic anhydride (PA) without the observation of any side reactions. The average Mn of the produced poly(CHO‐alt‐PA) climbed to 94.5 kDa with low polydispersity (Ð=1.19). Furthermore, an unprecedented turnover number of 9900, equivalent to an efficiency of 7.4 kg of polyester/g of catalyst, was achieved at a feed ratio of CHO/PA/catalyst=20000:10000:1 at 150 °C. Kinetic studies, crystal structure analysis, 11B NMR spectra, and DFT calculations provided mechanistic justification for the effectiveness of the catalyst system.