No you're right... I wasn't more clear about that. I'd probably still build a "hot box" for the miners to spout hot air into, and vent that out separately.
So the intake for the geo system would be ambient temp air from the non-hot box part of the room, and then the outflow "geo cooled" air would be directed more closely towards the intake on the miners themselves.
I'm probably not explaining this well, but I definitely wasn't implying running the hot miner air through that.
Am I missing something in the part of forcing hot air in the ground (down) and pulling cold air out (up) with small fans?
Wouldn't it be easier to simply force the air from the outside at ground level though this pipe network and in your shack at floor level and let the hot air simply go up and out with a single fan?