I was getting this sound too, after I found that my antifreeze level was really low I’ve added more and it went a way.
Check the level of your antifreeze.
Hmm, interesting. Thanks for the option, I never would have though of that, I will have to check it out and let you all know if it works!
Did you ever solve this issue? My 2000 GS300 has been making the same noise.