In this study, electrically insulating polyolefin elastomer (POE)-based phase change materials (PCMs) comprising alumina (Al2O3) and graphene nanoplatelets (GNPs) are prepared using a conventional injection moulding technique, which exhibits promising applications for solar energy storage due to the reduced interfacial thermal resistance, excellent stability, and proficient photo-thermal conversion efficiency. A synergistic interplay between Al2O3 and GNPs is observed, which facilitates the establishment of thermally conductive pathways within the POE/paraffin wax (POE/PW) matrix. The in-plane thermal conductivity of POE/PW/GNPs 5 wt%/Al2O3 40 wt% composite reaches as high as 1.82 W m−1K−1, marking a remarkable increase of ≈269.5% when compared with that of its unfilled POE/PW counterpart. The composite exhibits exceptional heat dissipation capabilities, which is critical for thermal management applications in electronics. Moreover, POE/PW/GNPs/Al2O3 composites demonstrate outstanding electrical insulation, enhanced mechanical performance, and efficient solar energy conversion and transportation. Under 80 mW cm−2 NIR light irradiation, the temperature of the POE/PW/GNPs 5 wt%/Al2O3 40 wt% composite reaches approximately 65 °C, a notable 20 °C improvement when compared with the POE/PW blend. The pragmatic and uncomplicated preparation method, coupled with the stellar performance of the composites, opens a promising avenue and broader possibility for developing flexible PCMs for solar conversion and thermal storage applications.