No suggestions but I can confirm you are not crazy. I too had a very similar noise. Car is in the garage over night so first thing in the morning no noise (I assume because it is a little warmer), however, afterwork and sitting in 0 degree weather for 9 hours, it made this weird high pitched noise like a tea kettly. I did let the car warm up until the light went off. 10 miles down the road, the noise stops...assuming because it got warmer.
Perhaps it is a faulty set point in the "warm enough to drive" sensor that turns the blue light off