the heat has to be passed on, you instilled energy into the air molecules but air is then a poor conductor of heat as we all know so expanding it again isnt enough, it has to touch something ie: other cooler air molecules or solid objects, you are blowing more hot air into the cabin than can be cooled so its cosey.
Sorry blabbering... squeeze it, it gets hot, expand it but it still contains the heat regardless until it is passed.
Isnt that heat called layton heat? (spelling)
