Polycaprolactone/polytrimethylene carbonate copolymers of different microstructures have been prepared in toluene solution under mild conditions by controlled ring-opening polymerization of e-caprolactone and trimethylene carbonate with methanesulfonic acid as catalyst. Sequential addition of the monomers led to the formation of well-defined di- and tri-block copolymers, demonstrating the ability of the catalytic system to cross-propagate. Simultaneous copolymerization yielded gradient copolymers as a result of the different copolymerization reactivity ratios and absence of undesirable redistribution reactions. DSC analyses showed a noticeable impact of the copolymer microstructure on the thermal properties.