Three‐dimensional boron nitride/graphene nanoplatelets (3D‐BN‐GNP) scaffolds were fabricated using an ice‐templating method and polyamide 6 (PA6)‐based composites were prepared by vacuum impregnation of caprolactam monomers into the scaffolds, followed by polymerization. The BN sheets in the PA6/3D‐BN and PA6/3D‐BN‐GNP composites display a predominant parallel alignment along the ice‐crystal formation constructing thermally conductive paths. The addition of few GNPs assists the dispersion of BN sheets in the PA6/3D‐BN‐GNP composites and repair the broken thermal paths caused by local agglomeration of the BN sheets. Consequently, GNPs play a morphology‐promoted synergistic role in the enhancement of the thermal conductivity of the PA6/3D‐BN‐GNP composites. The PA6/3D‐BN‐GNP composite prepared with 23.40 wt% BN sheets and 2.60 wt% GNPs exhibits the highest thermal conductivity of 2.80 W m−1 K−1, which is 833% and 33% higher than the values recorded for the pure PA6 and the PA6/3D‐BN composite at BN loading of 26.18 wt%, respectively. Infrared imaging analysis revealed that the surface of the PA6/3D‐BN‐GNP composite has a fast response to heating and cooling, suggesting the potential of the composites in thermal management applications.