Biodegradable shape-memory polymers have attracted tremendous interest as potential implant materials for minimally invasive surgery. Here, the precise control of the material's functions, for example, the switching temperature T-sw, is a particular challenge. T-sw should be either between room and body temperature for automatically inducing the shape change upon implantation or slightly above body temperature for on demand activation. We explored whether T-sw of amorphous polymer networks from star-shaped rac-dilactide-based macrotetrols and a diisocyanate can be controlled systematically by incorporation of p-dioxanone, diglycolide, or epsilon-caprolactone as comonomer. Thermomechanical experiments resulted that T-sw could be adjusted between 14 and 56 degrees C by selection of comonomer type and ratio without affecting the advantageous elastic properties of the polymer networks. Furthermore, the hydrolytic degradation rate could be varied in a wide range by the content of easily hydrolyzable ester bonds, the material's hydrophilicity, and its molecular mobility.