This article describes a green approach to the transportation and encapsulation of lauric acid (LA), a natural food-grade phase change material (PCM), in polystyrene (PS) hollow fibers. By simply tuning the temperature, the obtained LAPS composite fibers achieved an unprecedented thermal energy storage capacity up to 81.6% of pristine LA. This capacity was higher than the reported values in the literature which were generally less than 50%. The thermally triggered nanocapillary transportation and encapsulation of LA did not alter the size and morphology of PS hollow fibers. Furthermore, the LA was contained inside PS hollow fibers, leaving the interfiber space and surface free of LA. Direct SEM observation, IR spectra, Raman spectra, XRD diffractograms, and simultaneous TGA–DSC thermograms of LAPS composite fibers proved that the amount of encapsulated LA declined with the elevation of temperature. The distribution of LA in PS hollow fibers was found to be homogeneous across the membrane by TGA and SEM. Further, the LAPS composite fibers demonstrated a robust cycling stability and reusability without notable deterioration of thermal storage capacity during 100 continuous heating–cooling cycles. Also, the composite fibers showed excellent structural stability without any fiber rupture or LA leakage during prolonged and repeated heating–cooling cycles.