In this study, modification of poly(adipic anhydride) through branching its chains was carried out via melt condensation polymerization with D-mannitol. The percentage of mannitol was varied (3, 4, 5, 10, 15, and 20 Wt.%) and the resulting copolymers were purified and characterized by FT-IR and 13C-NMR. These analyses indicated that linear chains of poly(adipic anhydride) can react with strong nucleophiles and dissociate to produce highly branched poly(adipic anhydride-co-mannitol adipate) which confirms the validity of the proposed mechanism. The copolymer’s molecular weight characteristics have been also examined using GPC analysis. Thermal properties of copolymers were also investigated using TGA, DTG, and DCS analyses. TGA/DTG revealed that the thermal degradation of copolymers proceeds in multi-stage decomposition, whereas the shift and pattern change of the melting point peak of DSC curves can identify the weight percentage of mannitol for homogenous copolymers. Two non-isothermal models, the Flynn–Wall–Ozawa and Kissinger methods, have been also employed to analyze thermogravimetric data collected from the thermal decomposition of the copolymers and found that Flynn–Wall–Ozawa method provides better results with R2 correlation up to 99.3%. The activation energy in the region of Tmax was determined and found that an increase in mannitol contents in copolymer has a positive impact on its thermal stability.