In this paper we describe the mechanical and biological features of a thermosetting polyester synthesized from glycerol and dodecanedioic acid named Poly-Glycerol-Dodecanoate (PGD). This polymer shows a glass transition temperature (T(g)) around 32 degrees C, and this accounts for its mechanical properties. At room temperature (21 degrees ) PGD behaves like a stiff elastic-plastic material, while at body temperature (37 degrees C), it shows a compliant non-linear elastic behavior. Together with biodegradability and biocompatibility PGD has distinct shape memory features. After the polymer is cured, no matter what the final configuration is, we can recover the original shape by heating PGD to temperatures of 32 degrees C and higher. The mechanical properties together with biocompatibility/biodegradability and shape memory features make PGD an attractive polymer for biomedical applications.