A mathematical modelling has been established in order to predict the weld pool shape evolution in the frame of stationary gas tungsten arc welding experiment. In this mathematical modelling, the heat flux was modelled with a Gaussian function. This heat flux represents the energy generated by the electrical arc and absorbed into the work-piece. An inverse approach is used for estimating the parameters describing this heat flux from the " measured " temperatures. The Gradient Conjugate Method is used for solving the inverse problem. An adjoin problem is also solved in order to compute the gradient of the objective function. The aim of this communication is to check numerically the feasibility of the inverse problem and its robustness to random measurement errors.