Chromebook would be ideal for this.
I have the asus c300 chromebook and installed linux on it, works perfectly.
You can see a review of chromebooks here: http://www.techradar.com/news/mobile-computing/laptops/best-chromebooks-top-5-chromebooks-in-the-us-1233696
It's silent, has long battery life and is cheap.
You can see how to install linux on a ...
The HP Stream 14 uses the A4 Micro-6400T APU, which is passively cooled. It is already discontinued, but it can still be found on some sites. It is quite limited in performance and storage, but it is the only one passive AMD laptop I have found (and I have been looking for quite a while).
The more powerfull (TDP (thermal dissipation power) in watt) the computer, the more you need to cool it down. You can combine one or several of these:
You can pick low energy components (CPUs). You can further underclock the CPU or undervolt it so it consumes less energy, hence heats less. Usually when the technology makes a new step (transistor size ...
Since no one else answered I will give the answer, as in the meantime I choose the "Ubiquiti Unifi 16-150W" switch. It has one (maybe even 2) fans, but they only come on at a certain temperature and at startup. I have never heard them running after startup in my case, but I only have 2 PoE devices.
There is a IPC2 (Intense PC) mini PC (and similar) which comes with 4th/5th generation of Intel® Core™ i7 Processors and it is compatible with with Linux and Windows.
Please check the product page at fit-pc.com about IPC2.
There is also fit-PC4 which is based on AMD G-Series APU (3 times the performance of the previous fit-PC3).
It's available in Amazon (...