Ah ha, warm gun into a gun sleeve normally does cause trouble.
On the trigger guard? The trigger guard is nickel plated so its basically impossible for it to rust up, maybe i read it the wrong way and its the trigger itself?
I'd just use some thin spray can oil like Barricade on a harder fabric like a ;egging from an old pair of jeans and scrub the barrel and other parts down good. Give it a good coat of oil after that.
www.ultracoatingsinc.com has some great rust protection called Gun Shield. Ive applied it to almost all of my rifles and hunting in flat out snow storms for hours "3 of those hours being lost lol" the 2 rifles we had in the field didnt have one speck of rust on them.