It's only the movement of air on the skin that cools people down, which is why a bus stopped in traffic in the blazing sun, or a tube train stuck in a tunnel is a nightmare. When moving, with decent ventilation, I will accept that aircon is not (as) necessary.
I also suggested air conditioning stations, or indeed just extracting heat. Anyone working in that field would know how to draw cool air in, and suck hot air out - simply because of the way in which the air moves (and warm air rising).
We have to accept that deep level tube trains can't remove the hot air and so trains won't be air conditioned, although for any line where trains go into the open (where they can heat up most, especially when stationary at the end of a line) then you could argue that trains could have air conditioning, but have it disabled automatically when approaching the underground sections.
I am sure that once underground, with sufficient cooling at stations and the train not being so hot in the first place, it wouldn't actually get anywhere near as hot before getting to the other end and being cooled again.