Mild steel welded products are widely used for their excellent ductility. Tungsten inert gas (TIG) welding is a high-quality, pollution-free welding process suitable for a base part thickness greater than 3 mm. Fabricating mild steel products with an optimized welding process, material properties, and parameters is important to achieve better weld quality and minimum stresses/distortion. This study uses the finite element method to analyze the temperature and thermal stress fields during TIG welding for optimum bead geometry. The bead geometry was optimized using grey relational analysis by considering the flow rate, welding current, and gap distance. The welding current was the most influential factor affecting the performance measures, followed by the gas flow rate. The effect of welding parameters, such as welding voltage, efficiency, and speed on the temperature field and thermal stress were also numerically investigated. The maximum temperature and thermal stress induced in the weld part were 2083.63 °C and 424 MPa, respectively, for the given heat flux of 0.62 × 106W/m2. Results showed that the temperature increases with the voltage and efficiency of the weld joint but decreases with an increase in welding speed.