I'll agree with you. But inbound to the gate with an engine or 2 running, you can power the packs off the engines. Outbound is a different story. By all means if the airplane is too hot fire it up!

Honestly though, I think you're getting wrapped around the axle for no reason. If its hot, start the APU. If the captain questions you, explain your reason (show him the ball sweat on your seat if you have to). If he is particularly difficult about it, see if you can get the FA on your side. If he is still being a pill, then I guess you'll have to decide if being a few degrees cooler is worth the aggravation of butting heads with this guy for the next 4 days. Pick your battles man. If it's that important to you or it affects safety, speak up! Otherwise suffer in silence.