Did the aux fan come on at all while idling? The cooling outlet temp sensor is what the aux electric fan runs off of.
A year or two ago, I replaced an aftermarket outlet temp sensor with a used genuine BMW one I had laying around and suddenly the aux fan became much more active at idle. The fan comes on more frequently than with the aftermarket sensor. I do have functional A/C which is always on, but the quality of sensor did make a difference in frequency and length of aux fan runtime.
As for the ocassional squeaks, might be good to check the condition of the pulleys, especially the idler pulley on the top alternator bolt. If they spin freely and make any noise, its a good idea to replace them before they decide to seize up and trash the new belts.