Does the air ever go back from cold to hot again?
If so, there might be air in the coolant system (not sure how you would get it out, though, other than draining and refilling).
Does the engine temperature gauge change when the air goes from hot to cold?
If you have a rear A/C, do you always get hot air from the floor vents in back even when the front goes cold? If so, this would narrow the focus to the front.