Thermally conductive but electrically insulating polymer composites are highly desirable for thermal management applications because of their wide range of utilization, ease of processing, and low cost. However, the traditional approaches to thermally conductive polymer composites usually suffer from the low thermal conductivity enhancement and/or the deterioration of electrical insulating property. In this study, using cellulose nanofiber‐supported 3D interconnected boron nitride nanosheet (3D–C–BNNS) aerogels, a novel method for highly thermally conductive but electrically insulating epoxy nanocomposites is reported. The nanocomposites exhibit thermal conductivity enhancement of about 1400% at a low BNNS loading of 9.6 vol%. In addition, the epoxy nanocomposites are still highly insulating, having a volume electrical resistivity of 10¹⁵ Ω cm. The strong potential application for thermal management has been demonstrated by the surface temperature variations of the nanocomposites with time during heating and cooling.