Cooling the stations is not an engineering challenge. It's a budget challenge. Installing and operating huge chillers is a solved problem.
Not correct in context. You cannot successfully chill air without having a place to vent the resulting waste heat.
Where, in deep tube lines, to vent the waste heat, is _not_ a solved problem. It _is_ an unsolved engineering challenge.
The heat has been accumulating there for decades.
As detailed here
https://en.wikipedia.org/wiki/London_Underground_cooling