As the movement for carbon neutrality spreads around the world, research on hydrogen energy is also being actively conducted. In the hydrogen value chain, liquefaction is a particularly energy-intensive process. Although the operating energy of the hydrogen liquefaction process can vary greatly depending on the season or regional cooling water temperature, previous studies have not taken this into account. In this study, we quantitatively identify the effect of the change in cooling water temperature on exergy destruction, specific energy consumption (SEC), and coefficient of performance (COP) of the liquefaction process. In addition, we propose a design improvement to reduce exergy destruction with the exergy analysis of multi-stream heat exchangers. A new design (auxiliary process) that reduces exergy destruction is proposed by analyzing the device where energy destruction occurs the most. When the cooling water temperature increases from 20 °C to 35 °C, there is a tendency for SEC and exergy destruction to increase and the COP to decrease. The new design with an auxiliary process shows a decrease in SEC and a reduced rate of increase in SEC in response to the increase in cooling water temperature. The base case without the auxiliary cycle shows that the SEC with cooling water of 35 °C is 14.66% greater than that with cooling water of 20 °C, while the proposed process shows the rate of increase of 9.70%. This means that adding the auxiliary cycle can improve the energy efficiency and increase robustness to variations in ambient conditions.