In this work, a temperature‐regulating and antimicrobial–antioxidant fiber membrane was fabricated using coaxial electrospinning technology. The tea tree oil (TTO) emulsion used as the core solution, polyvinyl alcohol (PVA) as the shell solution for coaxial electrospinning, has been demonstrated. Compared with the original PVA fibers, the average diameter of the fibers is increased after coaxial electrospinning, and the diameter increases with the core flow rate. The diameters corresponding to core flow rates of 0.05, 0.1, and 0.15 mL/h are 561, 597, and 849 nm, respectively. Via in vitro release experiment demonstrated that the quantity of TTO released from the composite membrane increased with the elevation of temperature. The inclusions TTO and polyethylene glycol give the film excellent antibacterial–antioxidant properties and a delayed thermal response. More intriguingly, core–shell fiber membranes containing TTO in the core part are effective in slowing down the formation of oxidation spots on the surface of banana compared with pure PVA membranes. Seven days after wrapping bananas with different membranes, the surface of banana in pure PVA film was full of oxidized spots, whereas banana in PVA core–shell fibers showed only one obvious spot.