Couldn’t you use the River Thames as a heat sink for the Tube? Similar to how power plants use rivers and other bodies of water for cooling.

A quick google search shows its often below 60F, so with the proper heat exchanger and cheap renewable power, you could slowly pump all of the heat (built up over 100 years) out of the surrounding Tube earth into the river for disposal.

If you can use the heat for a useful purpose, great! But it seems like there’s lots of ways to get rid of it and get the Tube temp down.

They've used Tyburn

>I am sure readers will have heard of the ground water project at Victoria Station – and it has been a success. No questions – it works, and works well. The system currently draws most of its cool water from the Tyburn river, which slightly leaks into the circle line – and is drained into a sump. That cool water is used to cool systems in the station at Victoria and is very efficient in how it cools the air for minimal electrical effort in pumping water.

I think using the Thames would involve a lot of plumbing and pumping.

I don't think the problem is finding somewhere to put the heat, but to get it out in the first place. The article says the heat is currently vented into the street.

This has been talked about in the past.