Note that the deep-level lines (specifically those with smaller tunnels) are not included in this development. The central line has very small tunnels and will continue to be hot and cramped.
The new trains, platform-edge doors, and air-cooling are being introduced for the Central, Bakerloo, Waterloo & City, and Piccadilly lines. The tunnels and trains will still be small, there's not much that can be done about that, but they will be cooler, safer and hopefully a little less cramped, due to the extra capacity provided by walk-through carriages.
I did read the article, so must have suffered some kind of mental failure. I don't expect any real improvement in temperatures on the central line. There is nowhere for the heat to go.
(Surely puzzlement is the appropriate response to a blatant factual error, not "wrong, wrong, wrong!". I mean, I know HN is a hangout for intolerant geeks but still...)
You can, but cooling the line means cooling far more than just cooling the train cabins - passengers only accounts for something like 5% of the heat dumped into the underground, the vast majority is things like braking. And so costs of standard AC is an issue.
You also need somewhere to dump the heat, and part of the problem is actually that even re-opening existing vents is tricky and/or costly to do when many of these lines for most of their distance are 20m below some of the most expensive real-estate in the world.