Temp difference is press difference.
Ooo...Ooo...Oooo... I want in.
Not really. Warmer air expands causing it to expel some mass from the top of the flue... so less mass in the flue, less weight in the flue... less pressure in the flue.
But what if the height of the flue was infinite so the air could expand without losing mass... no matter how hot the air became the weight in the flue would remain constant... hence, no pressure change.
Temperature is the mechanize by which the flue loses pressure, but it isn't the pressure difference.
Just sayin'.