The fan of my PC's Seasonic SS-380HB PSU started rattling, so I replaced it with a brand-new Seasonic S12-II 380. Based on the reviews on SPCR and other sites I expected the new model to be even quieter than the old one.

However, after I power up the PC, the PSU fan ramps up to what I guess is full speed in a couple of minutes and stays there. Needless to say, this makes a lot of noise. The old PSU never made this amount of noise, even with a rattly fan.

Any suggestions as to what might be wrong here?

There's a chance that the temperature sensor is simply faulty. I'd check with the seller or the manufacturer for guidance.