Other thing you can do is just briefly remove the serpentine belt and run the engine (but really brief so you don’t overheat). If the noise is gone it could be the bearing on one of the accessories like the front water pump, alternator or P/s pump. Also check idler and tensioner pulleys. All have bearings that can wear. Spin each one by hand you can feel roughness with your hand.
that is the nature of these things. I had an occasional noisy exhaust flapper that drove me nuts till I figured out what it was, sounded like an engine knock. Found it with my mechanic's stethescope. Happened because I changed the style of exhaust system from the old OMC one piece V6 units to the newer 2 piece style used by OMC & Volvo.
Take the drive belt off and see if it goes away. This would narrow it down
Other thought id the spring loaded balls in the T above the thermostat housing. These restrict the flow of cooling water to the elbows. Maybe they arent opening and water through them makes a noise .
