it wouldnt overheat.. because if you're not doing anything with the pc, its running idle anyway the only thing would be the the Fans (and perhaps the HDD drive) wearing off faster.
as for the question.. I turn mine off when I go to bed. cant sleep with it turned on anyway. (its not loud, but it just annoys me enough to keep me awake )
one pc stays on 24/7 because its hosting gameservers.
my gameing pc is on pretty much 24/7 for downloading.
other pc in the house usually gets turned off at night.
and, a computer wont overheat if being left on overnight. 'overnight' is generally only 5-8 hours. so if you think 5-8 hours of being on will make it overheat, then you have some cooling problems. theres billions of computers all over the world that running 24/7 without problems. if you have the pc on all day and theres no problems then you could easily have it on all night without problems. day is generally around 16 hours compaired to 8 hours of night.
Only time my computer is not on is when I'm at work. Otherwise, I always leave it running. Only thing i'll turn off is all the LED lights. The fans though act as a night light for the living room hehe.