IIRC the main heat source is the breaking of the trains combined with the high frequency of them. I suspect that using many cars will still release a lot of heat into the tunnels.

Yes, with a small gap between it is harder to install proper cooling systems and also natural air movement it very limited for cooling purpose too.

The trains in the narrow tunnels push air around, so recent stuff like full height platform screen doors help improve conditions (allowing platforms to be air conditioned without having to air condition the tunnels)

i hope that with more modern technology that will be less of an issue.

vacuum tunnels would work too,

https://en.wikipedia.org/wiki/Vactrain https://en.wikipedia.org/wiki/Hyperloop

not sure if the hyperloop idea works for short distances.