Diagnosis
That's coil whine from the internal electronics, specifically the components regulating power to maintain the 365°F temperature. It's a common electronic noise, not a mechanical fault.
How to Fix It
First, try plugging it into a different outlet on a different circuit in your home. Sometimes poor or 'noisy' power from the wall can exacerbate the whine. If the sound decreases or stops, that was the issue.
If That Didn't Work
If the whine persists in all outlets and is constant, it's a characteristic of that specific unit's components. The sound often lessens as the styler reaches full temperature and the power draw stabilizes. There's no user-serviceable fix; it's an acoustic trait of the power supply.
Heads Up
This noise does not affect performance or safety. However, if the whine ever turns into a loud buzz, crackle, or is accompanied by a burning smell, unplug it immediately—that indicates a serious electrical fault.