If you play your games on Steam you could use <s>their in home-streaming service</s> [Steam Link][1] for ~50$,
put your computer in another room and stream to your monitor in your box room.

*Steam Link* doesn't produce any warmth that matters, it's as small as a hard drvie and has inputs for 3 USB-devices, LAN and W-LAN. HDMI as output.

I believe Steam lets you stream non Steam games too.


  [1]: http://store.steampowered.com/app/353380/