The powder bed fusion (PBF) process is a type of Additive Manufacturing (AM) technique which enables fabrication of highly complex geometries with unprecedented design freedom. However, PBF still suffers from manufacturing constraints which, if overlooked, can cause various types of defects in the final part. One such constraint is the local accumulation of heat which leads to surface defects such as melt ball and dross formation. Moreover, slow cooling rates due to local heat accumulation can adversely affect resulting microstructures. In this paper, first a layer-by-layer PBF thermal process model, well established in the literature, is used to predict zones of local heat accumulation in a given part geometry. However, due to the transient nature of the analysis and the continuously growing domain size, the associated computational cost is high which prohibits part-scale applications. Therefore, to reduce the overall computational burden, various simplifications and their associated effects on the accuracy of detecting overheating are analyzed. In this context, three novel physics-based simplifications are introduced motivated by the analytical solution of the one-dimensional heat equation. It is shown that these novel simplifications provide unprecedented computational benefits while still allowing correct prediction of the zones of heat accumulation. The most far-reaching simplification uses the steady-state thermal response of the part for predicting its heat accumulation behavior with a speedup of 600 times as compared to a conventional analysis. The proposed simplified thermal models are capable of fast detection of problematic part features. This allows for quick design evaluations and opens up the possibility of integrating simplified models with design optimization algorithms.