When l start my Civic, it makes a funny whistling sound in the front left. There is a cable that turns there, so l do not know if that is what is making the noise. Why would that cable make noise? Could it be something else?

The noise disappears when the car has warmed up.

It is a 2004 Civic with 96,000 Km (60,000 miles).

belt ???
water pump ??? (sometimes it squeals when bad)
ac belt ???

sounds like a belt tensioner is way too tight & when the car warms up, the belt expands a bit relieving some of the tension on the belt causing the whine to cease. This could eventually cause the belt to become worn to the point where it snaps have a mechanic examine this if u dont feel u r up to the task of adjusting this yourself.

Or the belt itself has just become brittle & stiff, once it warms up it softens up lessening the slippage on the pulleys

could just need adjustments, could need replacing. neither one should cost much belts r usually pretty cheap

Your serpentine belt may be too tight.