So, I went on with my upgrade and installed an Asus Strix GTX 970 (Overclocked)... The results look even more amazing ! The GPU is litterally stuck at 65°C running Prime95 + Furmark, with all the fans at their minimum (~500 RPM for the CPU and the case fans, 850 RPM for the GPU fans).
There is some coil whine when running Furmark, though, but I didn't notice anything when running real-world applications.
Another problem : for some reason, I cannot force GPUTweak to use my User Defined Settings, it always reverts to the default ones. Furthermore, I cannot go below 40% of the fan speed (~1100RPM), whereas if I leave it in Auto mode, it starts spinning at 30% (~800RPM). Trying to use the user defined mode ends up in poor hysteresis management and the fans spend their time turning on and off (0%/40%). The default settings are fine : the fans are off in all situations but gaming, where they do not go above 30%, and I cannot hear them.
Overall, an amazing card in an amazing case !