Basil, I certainly appreciate your mindset. Even if a small and inexpensive system has a minor effectiveness, if it can be done fairly cheap with DIY labor, it is certainly better than nothing.
If you are discharging to the same well that you are drawing from, there may not be any circulation with the aquifer, and your single well would warm quickly enough so as to be not be worth the digging.
Rain will percolate down through the soil across a large area, until it hits the highest sandy layer that is just above a layer of clay. The water will then spread out in a fairly flat shape.
If you drew water from a well on one end of your property, and discharged it to a well on the other end, the height of the water level in the discharge well would push water through the sandy layer, using a large mass of the soil as a heat sink.
I wouldn't put the two wells in a location with a house or any other important structure in between them, in case the higher-than-natural aquifer flow causes erosion and surface sinking, but it might be worth considering.
Best of luck