Just Curious, Would This Cause A Forest(er) Fire ?
My guess is that there is a solenoid whose job is to either allow or prevent removal of the key. It would make sense to allow key removal when the solenoid is not energized, so a car with a dead battery doesn’t exert a death grip on the key. That would mean that the entire time that the car isn’t in Park, the solenoid is energized, heating up the key as a harmless side effect. We hackers call that B.A.D.: Broken As Designed!
I was disappointed that they never once considered another potential source of heat, namely the giant ball of thermonuclear fusion in the sky known as the sun. I have personally had this experience of a very hot key and it is very strongly correlated with it being summer in the Arizona desert.
A car in direct sunlight becomes quite hot, especially if the air surrounding it is over 100 degrees. But it’s not just the air inside the car that the public service announcements warn us about, the car itself becomes hot. Including the ignition switch, and after you put your key into it. I received first-degree burns from the door handles on an 83 Volvo sedan growing up, and a similar process happens for anything else made of metal in the car.