More seriously: You might want to take a look at the shooting jackets that are used for the German "auflage" shooting. These usually have no sleeves, short sleeves or sleeves made out of a thinner material. These jacket will still support your torso but air can get in easier through the sleeve/armpit openings.
Look for the German word "auflage"
See here: http://www.schiesssport-buinger.de/s...g/Bekleidung_1
or here: http://www.keuchen.de/default.php/cPath/33_49_487