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I had a similar situation for a while were I used the 'ethernet of the powerline' solution with great success. Setting it up was easy, plus and work in fact, and it was fast enough for my needs, about 300 Mbs. It allows you to put you mini wherever there is a powerplug in the house.
 
Dude, I hate to say it, but your SO is really being a pain in the butt if she won't let you put a Mac Mini somewhere IN the house. My wife is pretty stern about aesthetics, but even she relented when I showed her the advantages of my HP Microserver (and even though it's small and quiet, it is WAY louder and larger than a Mini).

Time for a heart to heart, me thinks. No, I'm not saying to get rid of her; not even close! Just meet in the middle... that being said, I stick by my closet/entertainment cabinet/under something suggestion.
 
I'd use Peltier plates ( http://en.wikipedia.org/wiki/Thermoelectric_effect ) to cool mac-mini.

Code:
       +----------------+
   <~~ |   mac mini     |       //|//
  +----+-^^^^^^^^^^^^^^-+----+  ##H#
  |	                     +--====----
  |   cardboard box             ##C#     <~~
  +-------------------------------------

Hot air <~~ is sucked into cardboard box using the power of mini fan.

First it flows through pipe with radiator ##C# indide. Peltier plate === cools this radiator and heat is dispersed through another radiator ##H# with fan //|//.

Cool air goes through mac mini and is thrown outside. Voila!

The only thing to remember when using Peltier plates is that they require cooling powerful enough to disperse heat taken from cold-side radiator ##C# plus their own heat.
 
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