Implementing input parameters that match the experimental weld shape is challenging in LASER beam welding (LBW) simulation because the computed heat input and spot for temperature acquisition strongly affect the outcomes. Therefore, this study focuses on investigating the autogenous LBW of AISI 1020 using a three-dimensional heat transfer model that assumes a modified Gaussian heat flux distribution depending on LASER power (Qw), radius (R), and penetration (hp). The influence of such variables on the simulated weld bead was assessed through analysis of variance (ANOVA). The ANOVA returns reliable results as long as the data is normally distributed. The input radius exerts the most prominent influence. Taguchi’s design defined the studied data reducing about 65% of the simulations compared to a full factorial design. The optimum values to match the computed outcomes to lab-controlled experiments were 2400 W for power (80% efficiency), 0.50 mm for radius, and 1.64 mm for penetration. Moreover, the experimental errors regarding thermocouples positioning were corrected using linear interpolation. A parallel computing algorithm to obtain the temperature field reduces computational costs and may be applied in real-world scenarios to determine parameters that achieve the expected joint quality. The proposed methodology could reduce the required time to optimize a welding process, saving development and experimental costs.