Coaxial fiber membranes (CFMs) with poly(ethylene oxide) (PEO) encapsulated by biobased poly(L-lactic acid) (PLLA) were prepared by coaxial electrospinning technology, whose thermal management capacity was investigated. The coaxial structure and thermal reliability were studied by transmission electron microscopy, cycle-heating experiment, differential scanning calorimetry, thermogravimetric analysis, and wide-angle X-ray diffraction. Both heat conduction experiment and insulation experiment confirmed that the coaxial fibers have excellent thermal management capability. CFMs with PEO content of 49 wt % exhibit remarkable thermal stability and energy storage, while the thermal insulation efficiency could be improved by more than 21% comparing with a pure PLLA membrane. A Fourier equation corrected by the melting enthalpy of PEO can well describe the heating curves of CFMs, suggesting the primary and secondary effects from latent heat of PEO melting and reduced thermal conductivity of PLLA glass transition. The excellent thermal management capability and thermal stability underlies the wider application of CFMs.