Containers
tl;dr
Two coolers, each between ~4 and 12 liters/quarts. They don't have to be the same size.
The containers hold the pumps and the coolant, insulating them from the outside to maintain the desired temperature and keep them clean.
Circulation container
The circulation loop will need ~2 liters/quarts of coolant. More if you have a larger pad or longer hoses.
About half of the coolant is needed to keep the pump and optionally heater underwater. The other half will go into the loop once the pump starts working.
If you have a large cooler, it might make sense to either:
- put a smaller container inside the cooler to create a narrower reservoir, or
- put a volume-displacing object at the bottom of the container to reduce the volume so you need less coolant to cover the pump.
Cooling container
The cooling loop will need less coolant and therefore less volume. Most of the volume will be filled by ice packs. The water is just to fill the hoses, cover the pump, and make thermal contact with the ice packs.
Opening for hoses and cables
Once you have a working setup, it will make sense to cut part of the lid of the cooler to allow the hoses and cables to enter and exit the cooler. Plan which corner to use and consider the lid's locking mechanism, if it has one, before cutting.
Disinfection
Clean and disinfect the containers, volume-displacing objects, inner containers and any other components you put in the water.