A few degree temperature difference would take a ton of surface area and even more airflow to make much difference at all. Think big solar thermal collector on the shady side of the house. A differential controller could start and stop airflow.
Randen did what AC is talking about in his garage/shop some time ago. He rigged an air handler in the building to his ground loop, using the existing water coil and pump. What he ended up with was lots of drain water and a clammy/muggy shop. His ground loop was cooler than yours by some degree, since he lives in Canada. I know he messed around with multiple heat exchangers, pretreating return air with the straight water hx, then running that air through another colder hx before it was vented from the air handler. I can't remember how effectively it worked. It's all in one of his threads in the heat pump forum somewhere.
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