Get the model of a physical phenomenon based on experimental measurements will ensure that this model best described the reality that the ideal models, obtaining the dynamic equations which may extend to more accurately predict system behavior in the future. An optimization method based on Gauss-Newton method, which consists in reducing fitting error between a proposed model and a set of corresponding to a phenomenon described by a partial differential equation (PDE) data is proposed. The method will be applied to estimate the change of temperature distribution in a body from synthetic data (not obtained by direct measurement), knowing that the ideal model of this phenomenon is given by the equation of heat diffusion. Taking into account criteria such as precision, accuracy and speed of convergence, finite difference method is used to find the solution of the EDP.