The Supercomputer cooling system is a piece of the Supercomputer which prevents it from overheating. This system has only been mentioned in "A Lack of Goodwill" when X.A.N.A. William appeared on Earth and deactivated it, causing the Supercomputer to start to overheat. However, Aelita managed to restart the system before any major damage was done.
The Supercomputer Cooling System is likely either water or nitrogen-based, as indicated by the white fog that appears when it rises out of the case. Most computers require some form of cooling system to prevent heat damage to electronics, and most nuclear power systems also require cooling systems. Water is more likely, not only because it's easily obtained with the river nearby, but also because nitrogen cooling is harder to set up and almost never used in nuclear power systems.