Just so anyone else who may read this knows, you do NOT want to shut off your engine after 15 seconds in that situation just in case the transmission is in fact overheating. It is essential that the engine be kept idling in neutral or park for a while, say 15 minutes, if the light stays on, before any attempt at shut-down, before you'd want to rule out an actual overheat and call it a wiring issue. It probably was/is a wiring issue in this case (and not the sensor itself), but just in case...you don't want that fluid to burn just sitting in there.

Even though it was cold outside, the transmission may have been working pretty hard and they can and do get hot. Use low-range whenever you feel like you might need it. If I had to guess at it, four-high-open diff/AWD would probably be the most torturous on the transmission due to the added slip in the center diff. It could happen...

John B.