New tube for London stock

The TfL order confirmation press release quotes Siemens saying they "feature full air-conditioning - a real challenge in hot tunnels" here. August 2020 Underground News says: "Cooling systems will then need an upgrade at Earl’s Court, Knightsbridge, Green Park, Piccadilly Circus, Leicester Square, and Holborn, as will the York Road fan" Presume this is all included in the agreed budget for introducing the new trains. The video was 2014 release, a long way back in the design process.

Indeed, it looks like York Road is the last one left to do. But what about all those "cooling systems" to be upgraded? Do they currently exist? I only recall experimental systems, e.g. Green Park. How big is an "upgrade"?

So it appears that the whole 'air cooling' thing is a complete red herring. Presumably some PR oik thought it sounded 'cooler' than 'air conditioning', and didn't realise that what it actually, effectively, means is 'not liquid cooled'.

And the answer to the 'heat dumping' problem is literally nothing other than more effective fans.

9 shorter cars is a possible configuration.

9-car trains is not a typo! The current Picc trains are 6-car, but they replaced 7-car trains. The Bakerloo still has 7-car trains of similar length. The new trains have only double-doorways to ease boarding. It seems that the first, third and fifth cars from each end will be cut around where the single door pocket holds the open door, so the bogie can sit beneath the car. The second and fourth cars from each end will end around where the double door pocket holds the open door, with no bogies but they are supported by the adjoining cars. Of course, with outside hung doors like other modern stocks, there will no longer be door pockets.

Open car ends will allow passengers to walk through the train. With shorter than normal cars, there will be less relative movement than with current inter-car doorways, but more cars will be needed to make the same length of train. The idea for such radical trains dates back to 1998, although the PPP took away LU's right to design the Victoria line trains, so these will be the first trains they have ordered since:this article

It seems to me that the distance between bogies will probably be similar to former trains, and therefore the gap at curved platforms will be little changed.

The new trains will have much shorter cars and be able to fit the Bakerloo and Central but with varying train length of course, possibly 9 and 11 respectively.

I wonder whether these will have extensible floor plates, like much mainline stock, to fill the gaps. While these would constitute additional moving parts and failure points, presumably they could be as reliable as the doors, which these days seem pretty good. There would be many challenges such as variable distances (solvable by sensors), variable platform heights, cant (/slope), curvature (significant over the extensive door width); and there presumably isn't much available space in these low-floor trains. Also because of the wide doors they would be large and need to support a lot of weight, so bulky and heavy. But the curves at Bank, Embankment, Piccadilly Circus and others are lethal, and H&S must be on the case for new trains. Platform-based extensions are another possibility, which could involve a lot of chopping up; or perhaps combine that with general elevation to bring level boarding (assuming the trains themselves aren't lower, as with the S-Stock - but the tube stock is pretty low already). On balance I reckon platform work is probably preferable.

I think 'air cooling' is just what it says, whereas 'air conditioning' should more correctly apply to systems that actively control the delivered humidity as well as the temperature.
So the system on S stock is, and most likely the New Tube system will be, 'air cooling', but common usage has applied 'air conditioning' to simpler cooling systems. 

Space considerations come into this.

Air conditioning is possible on large trains, particularly when most of the track is in the open air. I believe S stock has air conditioning (but I may be wrong).

Tube stock doesn't have the space for full air conditioning with evaporators and condensers. Condensers would also generate additional heat in tunnels.

A promising set up was under consideration at one point. This involved "gel" blocks to be installed under seats. These would be chilled whilst in the open air and then cool the train in tunnels.

Unfortunately, the "gel" didn't meet LUL's fire safety standards and the project was abandoned.

LU are designing a prototype ‘active-gap filler’, for trial at Baker Street (Met) next year, which will be the first of its kind in the world, according to a staff circular "Our Plan, London Underground 2019/20". It is intended to eventually raise all tube platforms to provide level access, since tube gauge trains cannot be any lower.

Does anyone ever believe what's in a business case?
I suppose it depends on what you mean by "capacity".....Standing over the couplers doesn't seem to me to be very comfortable a means of travel,just cramming fish heads into the rounded corners of the sardine can.
Of course,if Central London offices stay as occupied as they are at present, 10tph may suffice......

The gap depends less on the length of the cars than the length between adjacent bogies. Current cars have the bogies at around the quarter and three-quarter positions beneath each car. The new shorter cars will have bogies near the ends of each car. Assuming even spacing of bogies along the train, I estimate 11.75 metres between bogie centres on the new Picc trains, compared with 11.124m on the current trains, so 5% longer and maybe slightly larger gaps at curved platforms! I believe most cars will be the same dimensions for the Central line, except for the end cars which will be adjusted to fit platforms. The current Central line trains have traditional car lengths with 10m between bogies, so 17.5% longer and probably larger gaps at places like Bank! That's progress?

How will the end cars be "adjusted"? Does this mean shortened? (thus reducing capacity)