Thermally conductive composites were prepared based on epoxidized natural rubber (ENR) filled with alumina, silica, and hybrid alumina and silica. The thermal conductivity and mechanical properties were assessed. It was observed that the interactions of polar functional groups in the fillers and epoxy group in ENR supported a fine dispersion of filler in the ENR matrix. The mechanical properties were improved with alumina, silica, and hybrid alumina/silica loadings. The ENR/Silica composite at 50 phr of silica provided the highest 60 shore A hardness, a maximum 100% modulus up to 0.37 MPa, and the highest tensile strength of 27.3 MPa, while ENR/Alumina with 50 phr alumina gave the best thermal conductivity. The hybrid alumina/silica filler at 25/25 phr significantly improved the mechanical properties and thermal conductivity in an ENR composite. That is, the thermal conductivity of the ENR/Hybrid filler was 2.23 W/mK, much higher than that of gum ENR (1.16 W/mK). The experimental results were further analyzed using ANOVA and it was found that the ENR/Hybrid filler showed significant increases in mechanical and thermal properties compared to gum ENR. Moreover, silica in the hybrid composites contributed to higher strength when compared to both gum ENR and ENR/Alumina composites. The hybrid filler system also favors process ability with energy savings. As a result, ENR filled with hybrid alumina/silica is an alternative thermally conductive elastomeric material to expensive silicone rubber, and it could have commercial applications in the fabrication of electronic devices, solar energy conversion, rechargeable batteries, and sensors.