Most elastomers suffer from poor thermal conductivity, which limits their further applications in various fields, especially for electronic devices. A common method to enhance thermal conductivity is to introduce thermally conductive fillers into elastomers. Unfortunately, thermal conductivity and compliance are often correlated and coupled: large amounts of fillers are required to increase thermal conductivity while damaging the compliance dramatically. In this study, we report thermally conductive and compliant polyurethane elastomer composites by constructing a tri-branched polymer network. The resultant polyurethane elastomer composites exhibit excellent superhigh stretchability (2000%), low Young's modulus (640 kPa), and low thermal resistance (0.11 K cm2 W-1). Experimental rheology and a theoretical tube model are employed to study the nature of the high compliant tri-branched polymer network. Furthermore, the remarkable flexibility of our elastomer composite and heat dissipation act as thermal interface materials in the thermal management of flexible electronics. These findings advance our understanding on the rational design of the polymer frameworks of thermal composites, improving our ability to predict, design, and leverage their unique properties for future applications.