There are still significant technical challenges associated with thermal management of electronic devices such as microprocessors. To improve heat dissipation performance of integrated circuits, a new Fibonacci phyllotaxis design of circular micropin fin heat sinks has been developed. To minimize both chip temperature and pumping power, a multi‐objective optimization technique was employed. The effect of design parameters such as phyllotaxis coefficient, pin fin diameter, and pin fin height on response parameters was numerically investigated using the full factorial design of the experiment. Artificial neural network was coupled with MO‐Jaya, to arrive at a Pareto frontier of optimal compromise solutions. The optimal set of design variables were found to be a height of 300 μm, a diameter of 122.6 μm, and a phyllotaxis coefficient of 130 μm with an inlet velocity of coolant 2.263 m/s. The selected optimum design was then investigated numerically, and the outcomes were compared to those predicted by the MO‐Jaya algorithm. The final confirmed response variables were a maximum temperature of 51.6°C and a pumping power of 0.191 W. The results show that the Fibonacci phyllotaxis structure of the micro pin fin heat sink has better heat‐dissipating performance.