I would strongly recommend against deionized (DI) water in any cooling system where you don't have the exact specifications of all materials in the loop (i.e. an off-the-shelf spindle cooling system).
DI water can be extremely corrosive to certain metals, plastics, and rubbers, especially at elevated temperatures. I suspect most of the major components would be unaffected, but you can't verify what the MOC is for everything you can't see:
- o-rings & seals
- adhesives
- solder/braze
- hose & pump internal materials
- internal coatings in spindle
My recommendation is to use
distilled water, not deionized. Distilled will achieve the objective of eliminating tap water mineral deposits, but without the risk of some system component you can't see or control being corroded.
(distant) 2nd choice would be reverse osmosis (RO) water. RO water is corrosive to certain metals, but
should be ok (ish) with most polymers.
Don't take my word for it - a simple search for "DI water corrosion" should result in a trove of chemical compatibility charts.