The high interfacial thermal resistance, poor dispersion, and insufficient contact of the fillers in polymer-based composites result in a lower thermal conductivity, restricting the development of heat conduction and dissipation industrial application. In this paper, bioinspired modification of poly(dopamine) (PDA) was applied to improve the interfacial adhesion performance of copper nanospheres (Cu) and carbon nanotubes (CNTs) in a poly(vinylidene fluoride) (PVDF) matrix. The synergistic effect of Cu and CNTs with different dimensions was beneficial to the formation of a continuous heat conduction network. Moreover, CNTs could reduce the distance that linked the adjacent Cu with the PVDF matrix and fill the defect vacancies. The PVDF composite with 30 wt % Cu and 5 wt % CNT achieved a high thermal conductivity of 1.44 W/(m.K) and a tensile strength of 95 MPa. The simulation analysis of the model indicated that the interconnected architecture of the CNT/Cu/PVDF/PDA composite reduced the interfacial thermal resistance by the bridging effect of CNTs. The long-term heat-transfer test with the corrosive medium showed that a high-performance polymer heat exchanger will have great application potential in the field of waste heat recovering.