I never heard a GE90 that I didn't like
and I have no idea what this subjective noise sounds like or what causes it
When talking about cool down in jet engines (large or small) some issues that come to mind are:
Depending on mass and shape different parts cool at different rates. and even the same part will cool faster at some of it geomentry areas than others.
Exampes are:
Case structures surrounding the rotor blades cool much faster than the rotor disks themselves burried deep in the center of the engine. Beacuse of this rate difference there could be a critical time when the blade tip clearenace is not optimum (too loose or too tight). The too tight part of it is at one time and the too loose part of it at yet another time.
too loose creates air distortions at the blade tips leading to rumbles and sometimes even a surge.
Too tight leads to binding at very low RPM and inability for a starter to overcome and/or excessive rub out which will show up as too loose when the rotors get to speed and equalize.
Then there is the effect of depth between the top of the engine and the bottom of the engine in the gas cavities where heat rises creating a bow in the rotor. This acts like a tire that has been allowed to sit too long leaving a flat spot and sets up harmonic vibration (noise) of some parts createing a cacophony of sounds until the spinning itself evens out the temperatures around the rotor.
All engines are subject to all the above, but to different degrees and rarely does once change a design just to change a subjective noise that only acts for a brief time.
Engine surge is of course to be avoided