Compact heat exchangers for heat removal has become one of the most effective cooling techniques. In this paper, numerical scheme to simulate conjugated heat transfer using additively manufactured heat exchanger is presented. A lattice structure as porous medium is used as effective cooling techniques for heat removal. The objective of these lattices is to transmit heat from the hot part to the cold part while letting the system benefit from two phenomena, heat conduction and convection. An optimization procedure using response surface method is proposed for the presented compact heat exchanger to improve the efficiency. This method was introduced in order to reach the global optimum with a limited number of computer experiments. Two optimization variables are identified: edge thickness for the lattices and the inlet velocity. A constraint optimization problem is formulated to maximize the heat flux through the heat exchanger. Hence at the same time, limiting the increase of the pressure drop and the decrease of the exit temperature.