Designers of electronic devices and telecommunications equipment have used different methods (e.g., three-dimensional chip architecture, comprised of a vertically integrated stack of chips) to increase the number of transistors on integrated circuits. These latest chips generate excessive amounts of heat and thus can reach unacceptably high temperatures. In this context, this research aims to develop thermally conductive liquid crystal polymer (LCP)-hexagonal boron nitride (hBN) composite films to replace the traditionally used Kapton films that satisfy the electrical insulation requirements for the attachment of heat sinks to the chips without compromising the heat dissipation performance. Experimental simulations show that the maximum temperature of the heater mounted with a hybrid heat sink reduced with increased hBN content. Furthermore, a sufficient slow cooling process in the fabrication stage of the LCP/hBN composite films promotes the fibrillation of LCP matrix, leading to highly ordered structure and promoted the composite's heat dissipation ability.