The air/heating system in my Dodge Grand Caravan (2011) has been turning on by itself. Sometimes, it will turn on repeatedly (full blast) three or four times within 10 minutes and sometimes it turns on literally every 5 seconds… I turn it off… 5 seconds later, it comes back on. This can go on for as long as I am in the car. Also, when it comes on and turn it down, it just turns itself back on full blast again. It seems to start in the back of the van (when it first comes on) and then when I get the rear off, the front stays on. Once I finally get that off, the rear will come again within a matter of moments. It doesn’t matter if I have the A/C or the heat on… It does it either way.
To me, this sounds like a problem with the Body Control Module, which–IIRC–has been problematic with these vehicles. Hopefully somebody else can recommend a lower-cost solution, but you may have to replace the BCM.