The structural designs obtained from topology optimization are typically highly complex and, thus, can only be fabricated using additive manufacturing (AM) as opposed to traditional manufacturing techniques. However, even in AM, manufacturability constraints must be considered during optimization to ensure defect-free manufacturing. A constraint prevalent in metal additive manufacturing is local overheating, which leads to defects such as part distortion and unfavorable mechanical properties and may lead to complete part failure. The geometry of the part has a large influence, as it affects heat conduction, which, if not adequate, results in excessive heat accumulation in certain geometrical features [1]. The zones prone to overheating can be identified by thermal simulations of the manufacturing process. However, these models are computationally expensive and thus not suitable to be part of the simulation-driven design optimization [2]. This paper proposes a computationally efficient geometric approach to detect zones that are prone to overheating by estimating the local conductivity in relation to the local material distribution in the vicinity of the point of interest. With a constraint to prevent these zones, embedded in a robust topology optimization formulation, our approach creates optimized structural layouts with recognizable heat conduction paths to the baseplate and are less prone to local overheating. High-fidelity AM simulations were conducted on the optimized designs generated by the novel geometry-based overheating prevention method. The numerical results have shown that the proposed geometric approach is feasible and computationally efficient for controlling local overheating in topology optimization for metal additive manufacturing in both 2D and 3D.