In this paper, we present a numerical solution for an inverse heat problem to estimate 2D space-wise coefficient in a parabolic system describing heat transfer. The inverse problem is recast into an optimization problem solved with a conjugate gradient method. This approach use the non linear optimization formulation by minimizing a cost function taking into account both the measured outputs of the system and the outputs calculated by means of the model. The solution is performed by using the free finite element software FreeFem. Numerical example is carried out to check the validity of the proposed method.