In the present work a genetic algorithm is proposed in order to optimize the thermal performances of finned surfaces. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by resorting to the finite elements method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. The genetic algorithm is then applied to the case of polynomial profile fins, in order to determine the polynomial parameter values which optimize the fin effectiveness. The optimum profile is finally shown for different polynomial orders.