To further expand on QuickAG's post, you need to isolate the sound and determine what is impacting it, either in volume or frequency (pitch).

An example would be if the sound is variable with road speed (ie, not dependent on engine speed), indicating it is either related to wind noise or the speed of a rotational item such as a wheel bearing or drive shaft.

Another example would be if it varies with engine speed, in which case you could reproduce the sound in any gear, at any speed, possibly even parked, by holding engine revs at the specific point.

It could be related to throttle position, or engine load, apart from the above two. There are also other variables, but those should serve to start.

You have already linked it to when the engine is cold. The next step is to narrow it down to what alters it, thereby leading you or your mechanic to the root cause.

Diagnostics 101. Hope it helps.

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