Some of the really low watt processors are pretty easy to work with.
My office is regularly 90 degrees or more in the summer time, and currently outside ambient temps are in excess of 105 degrees...
I would use a mid tower case with a front and a rear fan, and be sure that the video card was of the type that requires no fan mounted on it - Integrated video on the MB would be the best. Pick the coolest drives you have, and go for it.
Solid state - thumb drives - They would be pretty efficient in this application. I would still be concerned about capacity - especially when you bring up streaming.
Also - check out VIA's line of MB's. I believe they are probably perfect for your current set of specs... and I get the impression that they are rather tough! You would also be able to really reduce the footprint and power required with one of their MB's... And power is heat when you really think about it!
Have fun with it, and BACK IT UP!