ZimaBoard vs Mini/Tiny PC

In relation to my previous post I would like some insight of the heat and noise generated by mini/tiny PCs.

My main concern is noise as the system will be chugged in a drawer in my bedroom. As the previous post mentioned I have a budget of ~180$. Are these systems noisy? I first looked at the ZimaBoard as it is passively cooled but in terms of raw power it's come to my attention that it is overpriced compared to the CPU it comes with.

There is also the Misses factor. She will kill me for installing something that generates more or equal noise to those cheap electric fans people generally buy in the summer when the heat gets too much lol

So to sum up. Is there any option that is nearly completely silent and won't feel like dragging a boulder up a mountain in terms of speed?