I had a small form factor PC connected to my TV as an HTPC. Problem was, it was too big for where I wanted it to be, getting it "out of the way" meant putting it in a cabinet and cutting off the airflow, or booting and powering off the PC anytime I used it or was done using it.
Going to Roku solved all those problems from me quite easily, and since it's attached to the bottom of my tv via double-faced tape, it solves the "out of the way" and darn near un-noticeable.
I think I see where your heat problems are coming from.
It probably will call for heatsink modification.
I have a similar problem in my bedroom - I have a small laptop running win7 with a busted monitor though... picked it up for nothing. It is thin enough to fit under the bottom edge of the TV I have in there, and if it is turned so that the DVD player is forward, I really have no need to access any other part (there are 2 USB slots on the same side. I won't turn it on and off much, letting it sleep so that I can turn it on with WakeOnLAN, or I'll have to mod it for a switch on that side... still a pretty good solution.
I'd like to find an IR activated switch so I could turn them on with a clicker, but I haven't found a suitable candidate yet.
Another really good option is a Rasberry Pi, if you don't mind Linux...
But to each their own.