Ah ha - I knew there had been a similar post before, and now I've found it. But,
@WitleyPanda, look who posted it
So turn ignition on, heat rear windscreen and interior light comes on together with drivers door open warning light comes on. door IS shut. Start vehicle no change. Stop engine, try again same result. Eventually clears and sometimes no faults. 1.3 diesel 4x4 2012/13 Battery replaced several...
www.fiatforum.com
I'd still be checking for dirty connections or a broken wire between the door and the car, as its more likely to be in an area that moves (the hinge) or gets wet (inside the door or mirror), rather than in the warm and dry car interior. Does the wiring connecter between the door and the frame unplug? If so, I'd start there... Probably an earthing issue with the heated mirror and finding a route to earth back via the door lock switch and inside light. All these items, and the heated screens too, are actually turned on and off by the body computer (alongside the internal fuse box), so any small false current can lead to all sorts of oddness.