Four-dimensional (4D) bioprinting holds significant promise in precision medicine, enabling the emulation of dynamic changes in the human body and tissues to provide personalized treatments. Smart materials for 4D printing (i.e., responsive to specific stimuli) should exhibit properties, such as biodegradability, biocompatibility, and ease of processing, while also enabling the prediction of time-dependent behavior in programmed geometry. This study focused on the development of a body temperature-responsive shape-memory polymer (SMP). The thermal properties of the SMP were analyzed, and its biodegradability and biocompatibility were assessed through structures fabricated by three-dimensional printing techniques. The simulation calculated with this finite element (FE) solution was in good agreement with those measured in experiments. The findings contribute to our understanding of the behavior of SMP under various conditions, validating the effectiveness of the developed material for potential applications in precision medicine and 4D bioprinting. It has the potential for use in medical devices, such as catheters, stents, and artificial scaffolds, prepared by 4D bioprinting.