Do you have a depth and diameter, or round about, of them?
The calculation will be how fast heat can come and go from the walls of the cistern to the surrounding earth. The top 5 feet don't count.
The plastic liner will be an insulator.
And that will give an answer of how many btu can transfer in a day.
Rather than the loops of tube spread out, you will have a concentrated point of exchange.
What size furnace does the house have, 50,000btu, 100,000 btu, ?
I don't know much more than this, but it will be the focus of your design - can enough heat move through the plastic and cistern wall and surrounding dirt to keep up. Or will you just chill down the contents of the plastic liner and there you are, a cold hole in the ground.
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