Numerical simulations play a pivotal role in advancing fabrication processes and welding technologies, enabling the pursuit of sustainable practices. By employing the finite element method, crucial insights regarding welded specimens can be derived, encompassing deformed shapes, residual stresses, and even microstructural properties such as phase proportions and hardness. This study focuses on the modeling framework of welding processes, emphasizing the influence of various welding parameters on sustainable outcomes, including reduced environmental impact and enhanced resource efficiency. The investigation delves into the characterization of heat sources, accounting for temperature-dependent material properties and developing a comprehensive thermo-mechanical analysis. By incorporating sustainability considerations and utilizing our Finite Element (FE) model, we conducted further analysis to elucidate the stability behavior, aligning with sustainable objectives. By considering welding current, arc voltage, and welding speed as random variables with mean values and standard deviations, the study aims to identify a model that effectively accounts for the inherent randomness of the welding process. This research contributes to the growing body of knowledge on sustainable welding practices by merging numerical simulations, advanced modeling techniques, and sustainability principles. The outcomes of this study have the potential to inform industry stakeholders and decision-makers about the most effective strategies for achieving sustainable welding processes and minimizing the ecological footprint of the welding operations.