Quote from Retic
Also, how long can I play without it overheating?
Probably just occasionally touch it to feel if it's warm? If it is, then it's overheating, and you can simply stop using it to take a break while it cools down. I don't know how long it takes to overheat (never owned an Xbox console), but I have a sega genesis that overheats while using it often (or at least the power adapter). I don't think your X360 will be in any danger from overheating, as long as you make sure it doesn't stay overheating for long, and turn it off as soon as it does.
Again, I have never owned an Xbox console, so I cannot be 100% certain.