Different lines have different trains. The shallow level lines got new trains recently, because the lines were built using cut and cover (like in NYC), they were easily able to add air conditioning.

These trains are for some of the deeper level lines that were built by using tunnelling machine to bore deep underground.

Yes, on the lines that are not so deep, like the circle, metropolitan etc. Cooling these trains down is significantly easier than the very deep lines, as the heat from the AC can be chucked straight out into the open air. Deep underground there's nowhere for it to go.

The sub-surface lines (Circle, District, Hammersmith&City) are getting new stock (same sort of features - walk-through carriages, little bit taller). In the past few years automation was introduced on Victoria, Northern, Jubilee and I think Piccadilly lines that basically reduces the driver's role to opening and closing doors and emergency stops. This allows trains to run at higher speeds with less delay between seeing a signal and starting the engine.

I believe that was the Circle, District, Hammersmith/City and Met lines.