I was considering the same type of thing with a Velocity kit I'm working on. Vibration *may* not be too much of an issue, but it could be, if it allows the drive to work up a harmonic vibration.
Temperature shouldn't be too much of an issue. What's the operating ceiling of your plane? If it's below 6,000 feet, you might just run a conduit to the computer's compartment from the outside, giving it lots of cool air.
Operating system? I still hold that Windows XP is the most stable and reliable operating system Microsoft has yet put out, although Linux may be a better choice if you intend to use the PC to operate any critical instrumentation functionality. If you intend to pony up for the oldschool vacuum/pressure/voltage driven analogue guages, then why not build something to supplement them for display on a monitor instead? I say go for it!
I would be interested to keep up on your progress. Do you have a site to follow your progress on your plane? Please post a link or PM me with it if you do.
Hope my two cents didn't just lay about!