It has become the mainstream way to take advantage of the new carbon materials to modify polymer matrix to prepare thermal interface materials (TIMs) with excellent comprehensive properties for the modern electronic packaging materials. Yet, how to make full use of the properties of new carbon materials is still facing the severe challenges. Herein, thiol-functionalized carbon nanotubes/natural rubber (CNTs-SH/NR) TIMs with three-dimensional networks (3D) and covalently bonded filler/matrix interactions were fabricated through the surface chemical treatment as well as ice-templated approach. The results proved that CNTs-SH/NR TIMs could achieve a high through-plane thermal conductivity of 1.22 W m⁻¹ K⁻¹ with CNTs-SH content was 25 wt%. Simultaneously, it showed sensitive heat response capacity. The improvement of filler/matrix interface and 3D networks were of great importance in abating the total thermal resistance. Moreover, the method provide a novel route to design high-performance thermal conductive TIMs and apply for the thermal management of electronics.