Wound environment-responsive materials show great potential in skin repair. Herein, a temperature-responsive fibrous hydrogel was developed with the aid of the phase-change material of natural fatty acids. The extracellular matrix-like methacrylate gelatin (GelMA) nanofibrous hydrogels were fabricated via electrospinning and UV-crosslinking, followed by a depot of fatty acids/aspirin (ASP) encapsulated polydopamine (PDA). The as-prepared fibrous hydrogels showed a significantly faster ASP release at 40 °C compared with those of 25 °C and 37 °C, and an “on-off” drug release was achieved at heating and cooling cycles between 40 °C and 25 °C. The in vitro cell culture tests and in vivo wound healing study proved that GelMA-PDA-ASP nanofibrous hydrogels facilitated the cell growth and accelerated wound repair. Taken together, the thermosensitive drug-releasing nanofibrous hydrogel, showed a great potential for wound care.