Numerical simulation is widely used in all the fields of engineering to predict the results. In welding, various finite element tools are used to predict the bead profile, temperature distribution, joint strength, formability and metallurgical changes etc. With respect to the welding process suitable heat source model has to be assigned for numerical simulation. The most suitable heat source for Gas Tungsten Arc Welding (GTAW) process is the Goldack double ellipsoidal model. This model has few parameters like the width of the weld (a), depth of penetration (b), front profile ellipse (Cf) and rear ellipse profile (Cr). In this research article, the influence of these parameters and their effect on the temperature distribution is focused. For this purpose, based on the full factorial design welding simulations are performed with COMSOL. Later, the grey relational technique was used to find the contribution of these parameters. It was concluded from the full factorial method that; temperature variation is depended on the GTAW welding heat source parameters. At 95% confidence level, the width of the weld showed a major role in controlling the temperature. Moreover, the optimum combination of process variables obtained end with minimum temperature rise at a width of 0.7 mm, depth of 5.7 mm and frontal factor of 4.