Owing to the growing heat removal issue of modern electronic devices, polymer composites with high thermal conductivity have drawn much attention in the past few years. However, a traditional method to enhance the thermal conductivity of the polymers by addition of inorganic fillers usually creates composite with not only limited thermal conductivity but also other detrimental effects due to large amount of fillers required. Here, novel polymer composites are reported by first constructing 3D boron nitride nanosheets (3D‐BNNS) network using ice‐templated approach and then infiltrating them with epoxy matrix. The obtained polymer composites exhibit a high thermal conductivity (2.85 W m−1 K−1), a low thermal expansion coefficient (24–32 ppm K−1), and an increased glass transition temperature (Tg) at relatively low BNNSs loading (9.29 vol%). These results demonstrate that this approach opens a new avenue for design and preparation of polymer composites with high thermal conductivity. The polymer composites are potentially useful in advanced electronic packaging techniques, namely, thermal interface materials, underfill materials, molding compounds, and organic substrates. Polymer composites are fabricated by constructing 3D boron nitride nanosheet (3D‐BNNS) networks using an ice‐templated approach. The polymer composites exhibit a high thermal conductivity, low coefficient of thermal expansion, and an increased glass transition temperature at relatively low BNNS loading (9.29 vol%). This approach finds uses in the preparation of the polymer composites with high thermal conductivity.