The Active Electronically Scanned Array (AESA) radar systems, which utilize numerous small transmitter/receiver modules (TRMs) for enhanced detection and tracking, are becoming increasingly sophisticated as defense systems demand higher performance. This evolution has led to greater power consumption and significant heat generation from components like high-power amplifiers, phase shifters, and circulators within the TRMs. Efficient heat dissipation is crucial for maintaining radar performance and longevity. While advanced liquid cooling methods are effective, they are complex, costly, and impractical for space-constrained aircraft like fighter jets and drones. Air-cooled heatsinks, with their simplicity and reliability, are more suitable in these cases. However, traditional fin heat sinks, designed for single heat sources, may not effectively cool the multiple, unevenly distributed heat sources in TRMs. Optimizing pin placement to minimize pressure drop and target specific hotspots is essential for maintaining efficient cooling and ensuring reliable radar operation. To address these challenges, we developed a CNN-based multi-objective optimization process to predict the thermal performance of air-cooled heatsinks tailored for AESA radar systems. Using a numerical model, we analyzed the cooling efficiency and pressure drop across the TRMs and their structural components. A CNN model was then created to predict heatsink performance based on the numerical model's results. This approach led to a heatsink design with significantly reduced thermal resistance and improved cooling efficiency, particularly by optimizing pin placement to manage hotspots and minimize pressure drops across the TRM array.