This study investigates the effect of adding stearic acid (SA) on the thermal conductivity of polyamide 6 (PA6)/boron nitride (BN) composites. The composites were prepared by melt blending, and the mass ratio of PA6 to BN was fixed at 50:50. The results show that when the SA content is less than 5 phr, some SA is distributed at the interface between BN sheets and PA6, which improves the interface adhesion of the two phases. This improves the force transfer from the matrix to BN sheets, promoting the exfoliation and dispersion of BN sheets. However, when the SA content was greater than 5 phr, SA tends to aggregate and form separate domains rather than being dispersed at the interface between PA6 and BN. Additionally, the well-dispersed BN sheets act as a heterogeneous nucleation agent, significantly improving the crystallinity of the PA6 matrix. The combination of good interface adhesion, excellent orientation, and high crystallinity of the matrix leads to efficient phonon propagation, resulting in a significant improvement in the thermal conductivity of the composite. The highest thermal conductivity of the composite is achieved when the SA content is 5 phr, which is 3.59 W m−1 K−1. The utilization of a composite material consisting of 5phr SA as the thermal interface material displays the highest thermal conductivity, and the composite also demonstrates satisfactory mechanical properties. This study proposes a promising strategy for the preparation of composites with high thermal conductivity.