In this work, we prepared thermoresponsive shape memory epoxy thermosets by blending epoxy resin with poly(ethylene glycol-ran-propylene glycol) random copolymer (PEG-ran-PPG or RCP). Incorporation of RCP precisely tuned the temperature showing the shape memory effect of epoxy thermoset, which was established by dynamic mechanical analysis (DMA) and fold-deploy test. FTIR spectroscopy confirmed that the compatibility of the system is caused by intermolecular hydrogen bonding and only at high RCP concentration some phase separation starts. DMA and thermomechanical analysis provided evidence for the interactions of RCP chains with epoxy thermoset. The impact strength considerably increased especially for 30 and 40 wt % RCP modified blends. Furthermore, the blends exhibited good thermal stability in conjunction with excellent UV resistance.