A multi-pass laminar counterflow cooler or heater is an open duct divided into four subchannels with uniform wall temperature by inserting three impermeable sheets. Only the temperature of the flow stream varies along the subchannels. Improvements in heat transfer efficiency were investigated analytically with the use of eigenfunction expansions in the power series. The enhancement results in heat-transfer efficiency for two multi-pass devices (flow pattern A and flow pattern B) are represented graphically and compared with those in a single-pass device (without three impermeable sheets inserted) and those in a double-pass device (only one impermeable sheet inserted). Analytical results show that suitable impermeable-sheet position adjustments can effectively enhance heat transfer efficiencies for two multi-pass devices (flow pattern A and flow pattern B) compared with the efficiencies of single and double-pass devices.