A thermally activated shape memory polymer based on the mixture of polycaprolactone (PCL) and polydimethylsiloxane (PDMS) was fabricated into the nanofibre mesh using the electrospinning process. The added percentages of the PDMS segment in the PCL-based polymer influenced the mechanical properties. Polycaprolactone serves as a switching segment to adjust the melting temperature of the shape memory electro-spun PCL–PDMS scaffolds to our body temperature at around 37 °C. Three electro-spun PCL–PDMS copolymer nanofibre samples, including PCL₆–PDMS₄, PCL₇–PDMS₃ and PCL₈–PDMS₂, were characterised to study the thermal and mechanical properties along with the shape memory responses. The results from the experiment showed that the PCL switching segment ratio determines the crystallinity of the copolymer nanofibres, where a higher PCL ratio results in a higher degree of crystallinity. In contrast, the results showed that the mechanical properties of the copolymer samples decreased with the PCL composition ratio. After five thermomechanical cycles, the fabricated copolymer nanofibres exhibited excellent shape memory properties with 98% shape fixity and above 100% recovery ratio. Moreover, biological experiments were applied to evaluate the biocompatibility of the fabricated PCL–PDMS nanofibre mesh. Owing to the thermally activated shape memory performance, the electro-spun PCL–PDMS fibrous mesh has a high potential for biomedical applications such as medical shrinkable tubing and wire.