I'm using my nuc (7i7BNH) for many things and one of them is to listen to music. I'm an audiophile, listening to music at low levels where every noise is noticeable and annoying. I upgraded to NUC7i7BNH from my old and trusty mac mini (2013). I can say that the nuc is lot more noisy compared with the mac (which has mechanical HDD and fan, while the only mechanical moving part in the nuc is the fan).
So I started looking for solutions and discussing the problem with the manufacturers of the fanless cases (cause that's the only acceptable solution if you want totally silent NUC).
Without further testing (as the cases are still traveling to my location) and based on the technical parameters available online + the test results and information shared by the manufacturers, if you want completely silent NUC, and don't want to worry about issues if you load it for extended period of time, get the slowest nuc (7i3) and the best cooling solution (the manufacturer claims that it's their Plato X7).
I have no idea what will happen with the NUC warranty if you choose to go with custom case, but if this voids the warranty, then why Intel is not providing such solution so we can buy it.
There are better solutions compared to the Plato X7, but lot more expensive so I haven't done any research on them (because of the price).
I'm not advertising any product, just sharing my findings so far in my research to have completely silent NUC.