According to an aspect of the present invention, implantable or insertable medical devices are provided, which contain one or more biodegradable polymeric regions. These biodegradable polymeric regions, in turn, contain one or more polymers, at least one of which is a biodegradable copolymer that includes: (a) one or more amorphous polymer blocks that display a glass transition temperature below 37° C. and (b) one or more amorphous polymer blocks displaying a glass transition temperature above 37° C.
