I have this same issue. Today, in the morning, about 50 degrees out, I was able to roll the car down a slight hill with the engine off and I heard this noise. Like you said, mine gets better when the car warms up. I do still hear it when it warms up, but not nearly as loud as when it is cold. I am going to put my go pro in the engine bay somewhere and see if I can see where it's coming from.