Fuel cell-powered Autonomous Underwater Vehicles (AUVs) represent a growing area of research as fuel cells can increase their endurance. Fuel cells consume hydrogen and oxygen to generate electricity. Typically, the fuel cell generates as much heat as electrical energy, and heat management becomes a crucial parameter when designing AUVs. For underwater applications, there is a need to store both gases and several types of storage units with different characteristics exist which have impacts on the energy density and heat behavior. This study aims at including the heat properties of the storage units in the design process of fuel cell-powered AUVs. A heat balance over the energy system of an AUV is calculated for each combination of hydrogen and oxygen storage units. In addition, a multi-criteria decision-making analysis is conducted, considering the calculated total heat, the specific energy, the energy density and the volumetric mass of each combination of storage units as criteria, enabling a comparison and ranking them using two objective criteria weighting methods. Results show that the fuel cell is the major contributor to the heat balance, and that the combinations of liquid oxygen with liquid or compressed hydrogen can be relevant and suitable for underwater applications.