Recent reports indicate that if London were to warm up much more (it is currently 12C/20F above normal for April), the subway/underground system would become unusable for the warmer months of the year.

For reasons best explained here it is not considered feasible to cool it.

So, they don't even air-condition the trains in London. I didn't know that.

Just so everyone is clear about NYC, all the trains have air-conditioning. It's a real bear when you're standing on a platform (station) on a hot summer day and the train is pumping out hot air from its AC system, sometimes while the doors are open.

What NYC is considering doing for the 2nd Ave subway is to air-condition the platforms themselves. Where all that waste heat from the trains will go is another question.

I can only speculate how much more attractive an air-conditioned platform would be. I will say that many trains are overcrowded as it is, without the luxury of platform AC. I doubt the incremental increase in passengers would be significant. It would primarily relieve over-crowding on the Lexington Ave lines.