Your hand dug well has a lot more capacity than (3) drilled wells into the earth (2200 gallons versus 900 gallons), but you lack the surface area to transfer that heat adequately like a narrow, but deep drilled well. What would probably happen is, you would just chill the water down in the winter as you tried to heat the garage, and in the summer slow heat the water in the well as you tried to cool your garage.
If you lived in Maine like I do, you probably could chill your garage in the summer because the water temperature here below frost line is 57 degrees, and by the time heat from the garage was transferred to the water, a well insulated garage would be chilled to a comfortable level, but heating a garage in the winter would be tough. Even well insulated, trying to heat a garage with a 2200 gallon "tank" heated to 57 degrees would be a tall order, and even if it could, it would still be 57 degrees. Better than -20 below outside, but not exactly a humans preferred temperature of 70 degrees either.
Would it be worth it though to take the garage from -20 degrees to 57, then supplement the heat with another traditional heating system? It may be..IF IT WORKED...because only a 13 degree rise in temperature would be needed. That is better than lifting the garage 90 degrees (from -20 to 70 degrees) for sure.
I am not sure if I was in your situation if I would or not. I say that because I have radiant heat and could easily build a
compost heating system with my sheep farm manure, but I don't. Why? because for half the amount of time and labor I can just cut 4 cord of
firewood and
feed my woodstove. So it is not that it cannot be done, or not really help in heating your garage, but a matter of...would it be worth it if a different way is easier and less costly?