Light Emitting Diode (LED) applications are increasingly used in various microelectronic devices due to their efficient light generation. The miniaturisation of the LED and its integration into compact devices within the weight limit have resulted in excessive heat generation, and inefficient management of this heat could lead to the failure of the entire system. Passive and/or active heat sinks are used for dissipating heat from the system to the environment to improve performance. An ANSYS design modeller and transient thermal conditions were utilised in this study to design and simulate the LED system. The modeller performs its function by utilising the Finite Element Method (FEM) technique. The LED system considered in this work consists of a chip, thermal interface material, and a cylindrical heat sink. The thickness of the Cylindrical Heat Sink (CHS) fins used in the investigation is between 2 mm and 6 mm, whilst ensuring the mass of heat sinks is not more than 100 g. The input power of the LED chip is between 4.55 W and 25.75 W, as required by some original equipment manufacturers (OEMs). A mesh dependency study was carried out to ensure the results were synonymous with what can be obtained practically. The simulation results suggest that the power ratings did not affect the thermal resistance of the CHS. In addition, the thermal resistance increased with the increased thickness of the CHS fin. The efficiencies of the heat sink were found to increase with an increased thickness of the cylindrical fin and the accuracy between the calculated and simulated thermal efficiency ranges from 84.33% to 98.80%. Evidently, the CHS fin of 6 mm thickness is more efficient than the other CHS fins, as depicted in this study.