**6. Conclusion**

In this chapter, we have considered an optimization problem for a heat distribution in order to get a suitable thermal environment. We have performed the asymptotic expansion of the proposed shape functions with respect to the insertion of small coated inclusions. We have used a one shot algorithm based on the topological derivative to solve numerically the optimization problem. Numerical results are presented showing the efficiency of method. The proposed method can be extend to solve practical problems, like the thermal optimization of electrical multicables.
