You are heating your working fluid to a temperature equal to what's ambient within the heat exchanger, which takes the longest possible time of any heating this exchanger can perform. (Think it over.)
For the exchanger to operate continuously - that is, to sustain outflow at final temperature equal to inflow at initial - this means you need a lot of piping, because however many CFM of water at 10° (or whatever) come in, you need to supply exactly that many CFM at 30° out.
All that piping takes volume, which has to be excavated out of the clay in which has been sunk the heat we're striving to remove. There's no moving that without some heat exchanger, after all. So we're still stuck expressing time basically as volume, which is perhaps the worst possible misfortune when working underground. (Caissons can be built and pumped dry, where earth must be dug.)
Perhaps you're thinking of a cooling jacket lining the tunnel bore. This would make sense but will only operate at a net energy cost, because to sustain livability you're going to need to exchange heat outside the system and supply, effectively, refrigerant. From plants all over town...
I suppose it's odd to use cubic feet per minute and degrees Celsius at once. I polled Gemini three times and received three unique answers varying only in relatively insignificant digits, so feel confident expressing the conversion factor thus: one cubic foot per minute is about half a liter per second.
You are heating your working fluid to a temperature equal to what's ambient within the heat exchanger, which takes the longest possible time of any heating this exchanger can perform. (Think it over.)
For the exchanger to operate continuously - that is, to sustain outflow at final temperature equal to inflow at initial - this means you need a lot of piping, because however many CFM of water at 10° (or whatever) come in, you need to supply exactly that many CFM at 30° out.
All that piping takes volume, which has to be excavated out of the clay in which has been sunk the heat we're striving to remove. There's no moving that without some heat exchanger, after all. So we're still stuck expressing time basically as volume, which is perhaps the worst possible misfortune when working underground. (Caissons can be built and pumped dry, where earth must be dug.)
Perhaps you're thinking of a cooling jacket lining the tunnel bore. This would make sense but will only operate at a net energy cost, because to sustain livability you're going to need to exchange heat outside the system and supply, effectively, refrigerant. From plants all over town...