2009 MKX V6 has high pitched engine whistle, expecially when it is cold. May go away when at operating temp.

any part driven by the drive belt can do this

This is just a guess but I can think of only two things to check.
Exhaust system has a small leak.?
Or fuel pump is about to fail.?

possibly belt or bearing on alternator water pump ac etc.

This is a symptom of the inlet manifold gasket having a leak.The whistling is air going in through the small leak/hole in the gasket.With the throttle butterfly shut,air is getting sucked in the only way it can.Try tightening the inlet manifold bolts 1st.But more than likely the gasket needs replacing.Hope this helps

you may have a tensioner or idler pulley starting to go bad. They make a high pitched whistle when the bearings are on thier way.

Simply have someone slowly bring it up to 2000 rpm and listen with the end of a wooden broom handle touching the center bolt on each. Be careful not to get caught.

If you're not used to this you may be able to hear it whithout use of the "hearing aid"

Your drive belt may simply need dressing. You can buy this at almost any auto parts store for about 4 bucks. (dont use anthing else as you will cause the belt to stretch creating more issues)

Front brake caliper not releasing.Piston starting to seize

Sounds like a vacume leak, chk. for a cracked or broken vacume line or maybe one came off. Does it idle ruff? With it running open hood and listen for a low pitch whistle you may have to rev it up a little.

swng,
1) Is the service engine soon light ever on when engine is running?
2) Per your description I would look at the ECT sending unit. It sends coolant temperature information the the Engine Control Module for proper fuel delivery for cold engine start. It may have lost its calibration.
Let me know.
Regards,

check pawer steering pump belt mybe it is worn out or loose, also check the alteranator belt.