I've been toying with the idea of seeing how small I can make my main PC, which is based around an i5-2500k (Sandy Bridge). I use the CPU's integrated graphics (no external GPU), and only hard drive is a single 2.5" SSD. I have an unused 160-Watt PicoPSU which I believe could easily power this system. This is a 95 Watt TDP CPU, and I regularly max out all four cores. (And even if I replaced the CPU too, a comparable Haswell would be 84 Watts, so virtually similar cooling load.)
I'm sure I could cool it sufficiently cool it quietly in one of those "breadbox" style cases; anything that can fit a modern tower cooler should be adequate. But that's only about half the height of my current case, a Supermicro SC731i-300B. (Love this case by the way, just want a smaller system.)
What I'm wondering is, could I get away with something small enough to mount to the back of my monitor? Maybe something like this InWin BQS656
A small case means a small CPU cooler. And a small cooler may not cut it unless the fan spins quickly (which wouldn't be silent obviously).
Another consideration is that I do need an optical drive. If I mounted the main system to the back of the monitor, I'd just get a slim external optical drive.
The other idea is the smallest case that also allows an optical drive, something along the lines of this InWin BP655
it could silently cool a fully loaded 95W TDP CPU, then it could probably stand vertically right next to my monitor. But that's a big "if".
That case comes with a mini PSU. Using my PicoPSU, I could remove the stock PSU completely, and use the space for an extra fan... but I'm not sure if that'd be enough to keep things sufficiently cool quietly.