A multi-physics modelling of a static Gas Tungsten Arc Welding (GTAW) operation has been established in order to estimate the heat flux exchanged between the arc plasma and the work-piece. The heat flux was described with a Gaussian function where two parameters required to be estimated: process efficiency and radial distribution. An inverse heat transfer problem (ihtp) has been developed in the aim to estimate these parameters from experimental data. Levenberg-Marquardt algorithm was used as the regularization method in addition to an iterative process. The experiment consisted in a static spot weld with GTAW process. The weld spot was on for 5 s under Argon shielding gas, 2.4 mm pure tungsten electrode on a SS304L disc. Temperatures were measured with thermocouples and weld pool growth monitored with a high speed camera. The experimental data were used to solve the ihtp what led to values such as 0.7 for process efficiency and average radial distribution of 1.8 mm.