I do find it generally a little cooler in 1st class, I can only assume that's due to the door making it a more confined area to keep cool.
....
If the source if the conditioned air for that coach is within the first class area then I suppose it would be colder/warmer/more-conditioned than beyond the door.
....
Forgive me, I'm finding this a little hard to picture! Seat back tables generally sit with their hinges well above knee height. Unless you're so tall that to sit straight you would end up with your knees considerably higher than your waist that is!

.
Fair question. Well er yes the (folded) seat back table is only going to get in the way perhaps as I shuffle in and out of a seat. I have fairly long limbs for my height and while sitting there I was trying to visualise the folded table. I will have to try again next time I am in a 700 and hopefully realise the table must be higher than my knees.
Last Friday I had opportunities to travel on 700s again :-
I had a dose of the first class and find the armrests make a difference. I can lean on the armrests to stop myself tipping forward. Or are the first class seats a different shape/tilt ?. Perhaps I was just less tired this last Friday.
I did notice a few light thuds as the train moved - rear first class. I was in there on my own apart from a male who wished to share his loooong mobile phone conversation with me. I likened the thud to a whole panel that is slightly bowed flexing and the bow popping to the other side.
As for the passenger information I noticed that from St Pancras (where I got on) to Blackfriars the only info was destination and next stop (I do not think the tube service info was showing but not sure), South of Blackfriars we got the full info including the declass info - which I had been beginning to worry about !.
Going North earlier in the day 700044 (iirc) had refused to admit we had got past Blackfriars. Even as I left the train at Kentish Town it was still saying next stop Blackfriars !. I cannot recall where it thought we were from Mitcham Junction.
This mis-information is really bugging me. It devalues the information when it is working since, after all, how is someone supposed to decide if the information is correct or not ?. Just save money and not have it there at all in the first place. Or at least switch it off until it is known to be working.