Polymer‐based thermal management materials have many irreplaceable advantages not found in metals or ceramics, such as easy processing, low density, and excellent flexibility. However, their limited thermal conductivity and unsatisfactory resistance to elevated temperatures (<200 °C) still prevent effective heat dissipation during applications with high‐temperature conditions or powerful operation. Therefore, herein highly thermoconductive and thermostable polymer nanocomposite films prepared by engineering 1D aramid nanofiber (ANF) with worm‐like microscopic morphologies into rigid rod‐like structures with 2D boron nitride nanosheets (BNNS) are reported. With no coils or entanglements, the rigid polymer chain enables a well‐packed crystalline structure resulting in a 20‐fold (or greater) increase in axial thermal conductivity. Additionally, strong interfacial interactions between the weaved ANF rod and the stacked BNNS facilitate efficient heat flux through the 1D/2D configuration. Hence, unprecedented in‐plane thermal conductivities as high as 46.7 W m−1 K−1 can be achieved at only 30 wt% BNNS loading, a value of 137% greater than that of a worm‐like ANF/BNNS counterpart. Moreover, the thermally stable nanocomposite films with light weight (28.9 W m−1 K−1/103 (kg m−3)) and high strength (>100 MPa, 450 °C) enable effective thermal management for microelectrodes operating at temperatures beyond 200 °C. A highly thermoconductive, high‐temperature stable, and superflexible paper is fabricated via a rational construction of 1D rigid rod‐like aramid nanofibers and 2D boron nitride nanosheets (BNNS). Significantly, the rod‐like nanofiber morphology and rigid molecular chain can enable more efficient phonon transport through the 1D/2D configuration. Hence, the heat sink paper paves the way for thermal management of new and powerful components.