Implantable or insertable medical devices are described. The medical devices comprise (a) a therapeutic agent and (b) a polymeric release region that controls the release of the therapeutic agent upon administration to a patient. The polymer release region comprises a graft copolymer, which further comprises a main chain and a plurality of side chains. One of (a) the main chain and (b) the side chains corresponds to a rubbery phase within the release region at ambient temperatures, while the other corresponds to a hard phase within the release layer at ambient temperatures. Typically, the graft copolymer will comprise one glass transition temperature below ambient temperature and another second glass transition temperature above ambient temperature. Also described are methods for forming the above graft copolymers, methods for administering a therapeutic agent to a patient using the above implantable or insertable medical devices, as well as methods for making the above devices.