With the rapid advancement of microelectronics, electronic devices are evolving toward high power, high integration, and miniaturization. As their power density escalates to 1000 W/cm2, thermal management has emerged as a critical bottleneck constraining device performance and reliability. Polymeric materials are widely employed as thermal interface materials (TIMs) in electronics due to their excellent processability, electrical insulation, and mechanical properties. However, their intrinsically low thermal conductivity severely limits further development. Hexagonal boron nitride (h-BN) exhibits exceptionally high in-plane thermal conductivity and superior electrical insulation, rendering it an ideal filler. Nevertheless, h-BN nanosheets suffer from restacking and poor interfacial compatibility, leading to elevated filler-matrix thermal resistance and limited enhancement in composite thermal conductivity. Nanocellulose (CNF), as a renewable matrix, combines high specific strength, biodegradability, and favorable film-forming capability, making it an ideal substrate for TIMs. In this study, h-BN was first graft-modified with hyperbranched polymers (HBP) on its surface, followed by the fabrication of HBP-BN/CNF composite films via vacuum-filtration-induced self-assembly. Results demonstrate that the films exhibit exceptional thermal performance, with the HBP-BN 50 wt%/CNF system achieving a thermal conductivity of 16.941 W/(m·K)—representing an 9.36-fold enhancement over pristine CNF (1.809 W/(m·K)). This work offers a new strategy for developing high-performance bio-based thermal management materials.