With the rapid development of electronic devices and rubber tires, the industry has put forward new requirements for the heat dissipation of rubber components. With excellent thermal conductivity, oxidation resistance, and thermal stability, hexagonal boron nitride (h-BN) is often added to plastics or rubber as a thermally conductive filler, but is less effective when used directly. In this study, h-BN-K was prepared by direct modification of the mixed solution of KH-550, and KH-570, while h-BN-PK was prepared by co-modification of dopamine, KH-550, and KH-570. Two modified h-BN were added to natural rubber (NR) to improve the vulcanization properties, mechanical properties, and thermal conductivity. It was found that the tensile strength and thermal conductivity of 20 wt% h-BN-PK/NR composites were 30.6 MPa and 0.335 W/mK, which were 39.1% and 110.7% higher compared to pure NR (22.0 MPa and 0.159 W/mK), respectively. In addition, the addition of h-BN improved the thermal stability performance of NR to some extent. In conclusion, the h-BN-PK/NR composites provide a certain reference for the use of thermally conductive NR and suggest new ideas for heat dissipation of electronic devices.