Recently, thermal management has been drawing growing interest in resolving the heat accumulation issues in batteries and integrated electronic devices suffering from an increasing heat density potentially degrading the operating performance. Heat sinks have been intensively employed to solve the heat accumulation problem and the most critical factor for efficient heat dissipation has been found as conformal thermal contact between the device and the heat sink. Here, we introduce a new class of thermally processable composite adhesives maximizing the thermal contact by taking advantage of the plastic flow of polymeric composite at high temperatures. The composite adhesive material was composed with hexagonal boron nitride (h-BN), known for its high thermal conductivity, and a thermoplastic polymer, EVA-based hot melt adhesive resin. The material was manufactured using a twin-screw extruder compounding process, and the composite material was shaped through hot press molding. The thermal conductivity of the composite material, with filler composition adjusted, exhibited a thermal conductivity of 1 W/mK at a 30wt% loading. Using differential scanning calorimetry (DSC), it was determined that the material melted at 73 degrees Celsius. The key property of the plastic flow of the composite was systematically optimized through the thermal and rheological investigations of melting temperature and viscosity at high temperatures. Finally, the increase in the area of thermal contact and excellent corresponding thermal dissipation performance are demonstrated in the model system. That shows a reduction of approximately ~13% in heat generation was observed. Therefore, it is anticipated that the functional heat dissipation composite material can be effectively utilized in various conditions.