Low dielectric materials with high heat dissipation, low dielectric constant (Dk), and dielectric loss (Df) are urgently needed to address the issues of signal cross-talk and heat accumulation arising from the rapid development of modern communication technology and the integration of microelectronics. Polyolefins, as hydrocarbon polymers, have shown significant potential due to their excellent low dielectric properties. However, their low polarity and flexible structures limit their thermal conductivity and thermomechanical properties. In this study, we developed a method to prepare thermosetting polybutadiene composites with enhanced thermal conductivity and good dielectric performance by modifying hexagonal boron nitride (h-BN) and hydroxyl-terminated polybutadiene (HTPB) with thermally cross-linkable benzocyclobutene (BCB) groups. The properties of the resulting composites were tailored by varying the filler content. With 30 wt% of the BCB-modified filler, the composite (HB-30) displayed excellent dielectric properties (Dk = 2.70; Df = 1.67 × 10−3 @10 GHz). Meanwhile, it exhibited a thermal conductivity of 0.615 W/mK at 35 °C, which was 7.1 times that of pristine HTPB. It also showed significantly enhanced mechanical properties and thermal stability with a storage modulus of 2.7 GPa and a glass transition temperature (Tg) of 208.5 °C. This method proved effective for preparing polymer composites with enhanced thermal conductivity, heat resistance, mechanical properties and good dielectric properties, making them suitable for high-frequency communication applications.