Which system is primarily tasked with heat transfer management on a vessel?

The correct answer is the cooling system, which plays a crucial role in heat transfer management on a vessel. The primary function of the cooling system is to remove excess heat generated by various machinery, including engines and generators, which is essential for maintaining optimal operating temperatures and ensuring the safe and efficient performance of the equipment.

The cooling system typically utilizes a mixture of water and antifreeze to absorb heat from the machinery and then dissipates this heat through heat exchangers or cooling towers. This process prevents overheating, which can lead to equipment failure and safety hazards.

While the refrigeration system does involve heat transfer by removing heat from a space to maintain cooler temperatures, its focus is primarily on air conditioning and food storage, rather than overall heat management for the vessel's machinery. Therefore, the cooling system is the most appropriate answer in the context of managing the heat generated by the operational components of the vessel.