Metal additive manufacturing has matured to the point where it is used ubiquitously in all types of industries, not only as a rapid prototyping technology, but also as a complement to and even a potentially superior manufacturing method compared to conventional processes. For industries that require high precision and process control, laser powder bed fusion (LPBF) is the preferred technology for processing advanced alloys. Researchers have developed complex models to predict material behavior during laser–material interaction with high accuracy. However, these models are difficult to implement and often require specific software. Therefore, this study evaluates the applicability of algebraic models used in welding to predict variables of interest in LPBF in a simple yet effective manner. The models used are based on the fundamental equations governing heat transfer in solids. The predicted quantities include melt-pool dimensions, sub-grain microstructure, and solidification time. The models show high accuracy in predicting microstructural features in the processing of 316L stainless steel manufactured using LPBF. The scanning speed is confirmed as a dominant control parameter governing both melt-pool geometry and microstructural features. Incorporating remelting and multi-layer effects improves analytical models beyond single-track assumptions, providing a more realistic representation of LPBF thermal behavior and capturing the cyclic nature of layer-by-layer construction.