High-efficiency microchannel heat exchangers (MHEs) can remarkably meet the thermal requirements in many areas of technology. Several active and passive techniques can improve the efficiency of heat exchangers; the improvement enables engineering processes to decrease operational costs through waste heat reduction. In the present article, two different passive techniques are applied to improve the heat transfer efficiency of a counter-flow heat exchanger. To do this, four various microchannels with airfoil fins, circular fins, trapezoidal fins, and triangular fins are designed. First, the temperature distribution and effectiveness for each microchannel are calculated and compared with each other. Results of the comparison showed that the optimum structure belongs to the microchannel with trapezoidal fins. Second, BeO ceramic is utilized as the microchannel heat exchanger's material. At a given mass flow rate of 30.5 kg/h, the superior thermal features of BeO lead to more uniform temperature distribution, and also it makes an improvement of 219% in the effectiveness of MHE with trapezoidal fins compared to alumina-made MHE with simple channels.