The disclosed embodiments relate to a system that performs low-temperature desalination. During operation, the system feeds cold saline water through a liquid-cooling system in a computer data center, wherein the cold saline water is used as a coolant, thereby causing the cold saline water to become heated saline water. Next, the system feeds the heated saline water into a vacuum evaporator comprising a water column having a headspace, which is under a negative pressure due to gravity pulling on the heated saline water in the water column. This negative pressure facilitates evaporation of the heated saline water to form water vapor. Finally, the system directs the water vapor through a condenser, which condenses the water vapor to produce desalinated water.