Biodegradable and elastic poly(L-lactide-co-$varepsilon$-caprolactone) (PLCL) was electrospun to prepare nanofibers, and N-isopropylacrylamide (NIPAAm) was then grafted onto their surfaces under aqueous conditions using $^{60}Co-{gamma}$ irradiation. The graft yield increased with increasing irradiation dose from 5 to 10 kGy and the nanofibers showed a greater graft yield compared with the firms. SEM confirmed that the PLCL nanofibers maintained an interconnected pore structure after grafting with NIPAAm. However, overdoses of irradiation led to the excessive formation of homopolymer gels on the surface of thc PLCL nanofibers. The equilibrium swelling and deswelling ratio of the PNIPAAm-g-PLCL nanofibers (prepared with 10 kGy) was the highest among the samples, which was consistent with the graft yield results. The phase-separation characteristics of PNIPAAm in aqueous conditions conferred a unique temperature-responsive swelling behavior of PNIPAAm-g-PLCL nanofibers, showing the ability to absorb a large amount of water at < $32^{circ}C$, and abrupt collapse when the temperature was increased to $40^{circ}C$. In accordance with the temperature-dependent changes in swelling behavior, the release rate of indomethacin and FITC-BSA loaded in PNIPAAm-g-PLCL nanofibers by a diffusion-mediated process was regulated by the change in temperature. Both model drugs demonstrated greater release rate at $40^{circ}C$ relative to that at $25^{circ}C$. This approach of the temperature-controlled release of drugs from PNIPAAm-g-PLCL nanofibers using gamma-ray irradiation may be used to design drugs and protein delivery carriers in various biomedical applications.