Well, under load the PSU's fan should spin up. There is definitely no "fix" for that! Your post raises two questions in my mind:
1. Is the noise really from the fan? You call it "coil whine" which, if true, does not come from the fan motor. It might come from a real coil that is carrying a heavier load.
2. If the noise is really from your fan motor, is it actually excessive? If it really is noisy on a NEW PSU, check with the maker about a replacement. If it is an old PSU that has developed this noise problem recently, then the fan probably is worn out and needs replacement. Most PSU's have inside them relatively common case ventilation fan types, and you can replace yourself if you're handy.