1) Ground water is probably 50 to 60F (agree with Old).
2) The cistern might have flowing water from a spring and probably has a built in drain to control water level, without these features the water level would be variable and would probably flood the basement at some point and be dry at other times. If these assumptions are true, I would expel the water to an outside drain away from the cistern.
3) It will take a lot of water to create enough heat transfer to create much cooling in the house. I didn't do the math, but I would guesstimate, it would take 30 to 40 GPM and a large radiator to make much impact.
4) If the humidity has a dew point temperature higher than the water temperature there would be condensation from the cooling system.
It would be interesting to try this and see if it works.
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