Mine goes on every morning when the temperatures are low, and then turns off during the drive home when the air warms up. I am unconcerned.
Did your tire have damage?
They dunked it, and I had broken the seal on the rim and the seal on the valve stem. I had actually popped part of the hubcap off, so I knew I hit it relatively hard. Luckily, I didn't bend the rim. It was only $35 and under an hour at Dunn tire, whereas the dealership couldn't even get me in today. So given what it could have been, it was relatively painless. In fact, I got to work just as my new boss was also arriving, so I didn't miss much time.