In this study, a self-adjusting concentration of graphene thermal grease was developed to reduce the contact surface thermal resistance of 50 W light-emitting diodes (LEDs). The purpose was to identify an important type of heat conduction material with a high thermal conductivity coefficient, which can be applied to the contact surface of various high-heat sources or concentrated heat sources to achieve seamless heat transfer with an extremely low thermal resistance state. The contact heat conduction material conductivity reached the highest K value of 13.4 W/m·K with a 15 wt.% self-adjusting concentration of graphene grease. This material could continuously achieve a completely uniform and rapid thermal diffusion of heat energy. Therefore, we performed an analysis of chip-on-board light-emitting diodes (LEDs) with a highly concentrated heat source, which showed excellent heat dissipation under natural convection heat transfer. As such, this study achieved the natural convection mechanism and a heat sink volume thermal performance capacity of 473,750 mm3 for LEDs under 50 W, but those over 50 W require an enhanced forced convection solution and a heat sink volume thermal performance capacity between 473,750 mm3 and 947,500 mm3. If the heat source dissipation reaches 100 W, the volume capacity must be at least 947,500 mm3 for lighting equipment applications. In the experimental study, we also verified and analyzed the research data, including an analysis of the measured data, grease component wt.%, heat sink material selection, increase in heat sink volume, heat transfer path, and contact surface, a discrimination analysis of infrared thermal images, and an analysis of flow visualization, which were conducted to ensure quantitative and qualitative improvement, provide a mechanism for judging the technical performance, and provide research results to enable discussion.