The parameter sets used during the selective laser melting (SLM) process directly affect the final product through the resulting melt-pool temperature. Achieving the optimum set of parameters is usually done experimentally, which is a costly and time-consuming process. Additionally, controlling the deviation of the melt-pool temperature from the specified value during the process ensures that the final product has a homogeneous microstructure. This study proposes a multiphysics numerical model that explores the factors affecting the production of parts in the SLM process and the mathematical relationships between them, using stainless steel 316L powder. The effect of laser power and laser spot diameter on the temperature of the melt-pool at different scanning velocities were studied. Thus, mathematical expressions were obtained to relate process parameters to melt-pool temperature. The resulting mathematical relationships are the basic elements to design a controller to instantly control the melt-pool temperature during the process. In the study, test samples were produced using simulated parameters to validate the simulation approach. Samples produced using simulated parameter sets resulting in temperatures of 2000 K and above had acceptable microstructures. Evaporation defects caused by extreme temperatures, unmelted powder defects due to insufficient temperature, and homogenous microstructures for suitable parameter sets predicted by the simulations were obtained in the experimental results, and the model was validated.