Going from 75 degrees to 50 produces something like a 1.5 psi reduction. 85 -> 35 wound be closer to a 2psi drop. Water vapor increases the drop. Funny thing is searching for the calculation produces highly variable results.
Belichick specifically said he was not talking about atmospheric temperature conditions, but the conditions of the ball. Presumably whatever rubbing of the ball was necessary for preparation heated the air in the ball. He must have explained this in the most obtuse way possible to reduce the chance people call him a cheater for heating the air in the ball.
Exactly the same reason professionals in auto racing use filtered/pure nitrogen to fill tires, instead of traditional compressed atmospheric air.