Mine does a quick chirping/whirling noise when I push the clutch in quickly. It's only in the first few gears as you described, while the engine is under low load (not quite into any boost), and a quick sound. Maybe half a second long.
I just noticed it lately, but I think mine does it despite what temperature the engine or outside air is.
EDIT: I have no idea what it is, or if we are both about to die in a fiery death. I just ignore it though, for what its worth.