My gaming rig is in the basement hooked up to the gigabit LAN port of my wireless AC router. My thin, light, cool and quiet laptop is now my gaming rig right on the couch while we watch TV or whatnot.
In the same vein, if my kids want to play a game I have a cheap, quiet small form factor PC hooked up to the TV with some 360 controllers plugged into it, same deal. Stream away. No noise, no heat, and the gaming rig stays nice and cool (and comparatively dust-free in the unfinished portion of my basement.
Worth a look, especially since you mentioned you're a Steam user already.