The thermally activated shape memory response of polymeric materials results from a combination of the material molecular architecture with the thermal/deformational history, or 'programming'. In this work, we investigate the shape memory response of systems based on poly(epsilon-caprolactone) (PCL) so as to explore the adoption of proper chemical and thermomechanical tailoring routes. Cross-linked semicrystalline PCL-based materials are prepared by different molecular architectures starting from linear, three- and four-arms star PCL functionalized with methacrylate end groups, allowing to tune the melting temperature, T (m), ranging between 36 and 55 A degrees C. The materials' ability to display the shape memory is investigated by the application of proper thermomechanical cycles on specimens deformed at two different temperatures (23 and 65 A degrees C, i.e. below and above the T (m), respectively). The shape memory response is studied under dynamic thermal conditions in thermally activated recovery tests, to identify the typical transformation temperatures, and under isothermal conditions at given recovery temperatures, to monitor shape recovery as a function of time. All the specimens are capable of full recovery on specific thermal ranges influenced by both melting and deformation temperatures. Specimens deformed above T (m) are able to recover the whole deformation in a very narrow temperature region close to T (m), while those deformed at room temperature display broader recovery processes, those onset at about 30 A degrees C. Isothermal tests reveal that when the deformed material is subjected to a constant recovery temperature, the amount of recovered strain and the time required strongly depend on the particular combination of melting temperature, deformation temperature and recovery temperature.