Borisz put's it quite right and he remembers me that I've forgot a very very important aspect:
If you take the heat from the miners to the air, you will be heating the air.
Heat always travels naturally from hot surfaces to cold ones (never the other way around. People here in my country have the terrible saying that leaving the fridge door open, lets the cold get out. Terrible ignorance and terrible mistake. The cold never gets anywhere, it's the heat that gets in!!!).
But, you can create cold from heat, although...
If you use a Refrigeration cycle using the flywheel to power a compressor, you might get something, although the energy required would progressively be wasted and would induce lot's of friction on the engines piston, reducing even more the efficiency.
But that got me thinking... How about a reverse Rankine cycle?
But even so, that would be too much hassle and highly costly.
Even freezers are only efficient because they work in a closed box from where they slowly pump the heat out.
In a large scale mining, IF (and only IF) I had access to way cheap hardware, I'd prefer to create some custom cooling solution evolving some kind of heat pipe and a roof made of massive heatsinks exposed to the air, topped with a layer of dirt and grass that I'd be watering to keep it fresh so it would absorb heat, snow, dust, etc.
Or the walls would work like giant radiators.
Or have a river nearby and pump water too cool down everything.
I get your point, the sterling is cute, but since you can't move the heat too far away from the device, it would becoming less and less efficient.
But hey, don't give up!!!
I just would have to take a lot of reading (which I have no head to, right now) and do some calculations based on the air permeability, what temperature saturates the air, etc, etc.
Not easy!!!
