Its not the bloody cooler it is from the VRM to be more specific it is the chokes charging and discharging.
See the two little boxes next to the rectangular chip at the end its those. Typically most users don't notice this but a few with either very good hearing or very silent box do.
Since the plate doesn't cover them and just millimeters under the fan it is tricky to do mod cooling but any thin aluminum or cooper sheet and some arctic silver5 compound and your set. Just cut it to size and make sure that they don't touch any thing else. The arctic silver5 will act as glue and will harden over time while reducing the annoying noise.