You have several options here. First...fix it there is a ton of places to buy parts. Second, sell it as parts. Its worth more apart than together. Third put it in a new case or make it into another computer. A briefcase would be sweet as would an iMac style case.
As for cooling properties, the original case was designed the way it was for a reason, to help it cool itelf. You need to find a way to put the bottom case back on or create a new way to cool it with heatsinks. There is a ton of heatsink out there that will work, but the hard part is getting the to stay on. My advice is heatsink glue or tape with some sort of homemade bracket also. Putting the screen seperate is tough. You would need a power supply and to figure out what wires go where.
Good luck