that is one tiny case...
when you look at your GPU temps, what is happening there?
i had a Gigabyte G1 1080 that made this sound every time the fans turned on:
https://www.youtube.com/watch?v=JudXFqkoEmwthe card kept heating up while idle, so eventually it would hit the threshold (no matter if i set it to 45, 50 or 55°C) where the Fans turned on, but a "mild breeze" was enough to cool the heatsink down by 1°C ...then it turned off again for like 5 or 10 seconds until the GPU temp went that 1°C up again... and it did that on/off loop forever.
Solution one: custom fan curve, put it to 30% and you can't hear it...
Solution two: better airflow in your case so it doesn't heat up like that.
the Gigabyte card also had horrible Coil Whine, that Fan Stop LED was not indicating what the Fans were actually doing and i had an overall bad impression of the Gigabyte card this time so i send it back to the Shop and got an EVGA 1080 FTW instead. (which made an awesome impression, but now i have to deal with the VRM temperatures nonsense... *sigh*)
in the meantime i added 3 more case fans which brings me to a total of 6x 140mm Case Fans (all super silent at 5v), 1x 120mm CPU Fan (1000rpm when gaming, 500 when idle), the 120mm Fan in the PSU also has a Zero Fan Mode, just like the GPU. I seriously can't hear the PC anymore when idle... and even when gaming it is very negligible. (the noise the heater in my room makes drives me nuts, but that is a different topic)
pics ->
http://imgur.com/a/6ERQmfull excessive build log ->
http://imgur.com/a/FBDEoi also made the jump and threw out all my internal HDDs and the System is as silent as it possibly can be without Watercooling,
i've even put a noise dampening kit in there (not sure if that actually did anything, but it looks damn good and plugged a lot of ugly holes in the case).
anyway with your ...mini ITX? case i'm afraid you won't have many options to add case fans.
my GPU is now, after hours of being idle, at 33°C and 0 RPM (with the original bios which i intend to NOT update (i guess when you get your RMA back it will have the new BIOS with the aggressive fan curve already installed, so that will get louder), my thermal pad mod is awaiting shipping, that should be enough anyway.).
//edit: i almost didn't notice that (signed?) Captain Kirk picture on your desk :D