About 24K miles ago, the tranny was professionally flushed and refilled with synthetic. I will double check the air intake, but it doesn't sound like a turbo. It could be the fan clutch, but I don't think it has anything to do with the AC system as this occurs anytime, whether the AC is on or not.
First, I would be curious about the synthetic... generally that is only recommended in high stress racing or drag transmissions on occasion, not everyday usage. In some cases, using anything outside of the originally recommended fluid can be cause for concern with many of these new vehicles since the late 90s. They are designed with certain specifications and fluids to work properly.
Automatic Transmission Fluid Usage ATF+4 (Type MS9602)
2004 - 2007 (HB) Durango
NOTE: ATF+4® must always be used in vehicles that were originally filled with
ATF+4®. DO NOT USE ANY OTHER FLUID.
NOTE: ATF+4® is backward compatible with ATF+3 , ATF+2, and ATF+. Additionally,
ATF+4 can be used to top off vehicles that used ATF+3, ATF+2, or ATF+.
Sometimes simply removing the entire air intake hat, checking the seal around the air filter and other seals/connecting hoses can find it.
As for the AC system, it doesn't have to be in use or turned on inside to be affected, the belt is still turning the compressor which means it still monitors and charges the system and would still be affected.