In Metal Additive Manufacturing (MAM), support structures serve not only for mechanical supports but also for heat dissipation, preventing overheating in the melt zone. Although a high support volume aids heat dissipation, it significantly increases printing time, material wastage, and post-processing efforts. Additionally, contact area between the part and the supports often has higher surface roughness, which compromises part quality. This paper presents a novel density-based Topology Optimization (TO) technique for designing support structures optimized for efficient heat evacuation while keeping the part design fixed. First, a simplified MAM model, already established in the literature, is used to identify regions prone to overheating, referred to as ‘hotspots.’ This hotspot information is then used to formulate a TO problem that minimizes support volume while regulating the heat evacuation efficiency of the supports through thermal compliance which is defined as a constraint. For calculation of thermal compliance, a thermal load is defined using the hotspot information while the baseplate acts as a heat sink. To reduce post-processing costs, a concept of vicinity penalization is introduced, promoting the minimization of the part-support interface area. First, a set of 2D results is presented to demonstrate the method’s effectiveness and explain the influence of various parameters. Next, the TO algorithm is applied to a real-size 3D part and the results are discussed. Finally, the performance of the optimized supports is evaluated using a transient layer-by-layer AM simulation.