The powder bed fusion (PBF) metal additive manufacturing (AM) method uses an energy source like a laser to melt the metal powders. The laser can locally melt the metal powders and creates a solid structure as it moves. The complexity of the heat distribution in laser PBF metal AM is one of the main features that need to be accurately addressed and understood to design and manage an optimized printing process. In this research, the dependency of local thermal rates and gradients on print after solidification (in the heat-affected zone) was numerically simulated and studied to provide information for designing the print process. The simulation results were validated by independent experimental results. The simulation shows that the local thermal rates are higher at higher laser power and scan speed. Also, the local thermal gradients increase if the laser power increases. The effect of scan speed on the thermal gradients is opposite during heating versus cooling times. Increasing the scan speed increases the local thermal gradients in the cooling times and decreases the local thermal gradients during the heating. In addition, these simulation results could be used in artificial intelligence (AI) and machine learning for developing digital additive manufacturing.