Additive manufacturing (AM) has revolutionized part manufacturing, offering unprecedented design freedom and the ability to fabricate intricate structures. Computational design methods like topology optimization (TO) effectively capitalize on AM's design freedom. However, manufacturability constraints must be considered to ensure reliable manufacturing. A significant constraint is local overheating, prevalent in metal additive manufacturing, leading to defects, part distortion, and diminished mechanical properties. While overhangs are commonly associated with overheating, they are not the only geometric features prone to overheating. This thesis addresses the overheating issue in topology optimization by a novel geometric approach. Specifically, we propose to estimate the local conductivity around each element by evaluating the material distribution in its vicinity. This is then used to generate a pseudo temperature field (i.e., hotspot map) to assess overheating risks. Formulated as a constraint in topology optimization, our approach creates optimized structural layouts free of local overheating during additive manufacturing. Additionally, the approach is implemented in space-time topology optimization, limiting overheating risks by simultaneous optimization of structural layout and fabrication sequence. Compared with existing overheating prevention methods, the geometry-based constraint demonstrates significant computational advantages. Transient thermal AM simulations were conducted on the final designs obtained using the physics-based method from the literature and the novel geometry-based overheating prevention method. The numerical results have shown that the proposed geometric approach is efficient and effective in controlling local overheating in topology optimization for metal additive manufacturing.