The need of intelligent implant materials for applications in the area of minimally invasive surgery leads to tremendous attention for polymers which combine degradability and shape-memory capability. Application of heat, and thereby exceeding a certain switching temperature Tsw, causes the device to changes its shape. The precise control of Tsw is particularly challenging. It was investigated in how far Tg, that can be used as Tsw, of amorphous polymer networks from star-shaped polyester macrotetrols crosslinked with a low-weight linker can be controlled systematically by incorporation of different comonomers into poly(rac-lactide) prepolymers. The molecular mass of the prepolymers as well as type and content of the comonomers was varied. The Tg could be adjusted by selection of comonomer type and ratio without affecting the advantageous elastic properties of the polymer networks.