Go for it unless extermely overclocked time it burns out you'll be wanting anew one anyways I leave mine on overclocked to 4.5 ghz no problemo here. For months just have good ventilation good fans if you want to really be safe just add a above stock cpu fan I use the ultra x7 cheap and works great.
I do it all the time! I just take a few precautions (usually in summers) to make sure that the CPU does not heat up. I leave the fan on.
It won't matter if you keep it on the whole night. The only thing that would become an issue is electricity spikes which can also be taken care of if you have a good UPS and/ or spike guard. I have both, so no issues. My internet is not connected to the UPS, reason being that should your computer shut off abruptly in the missle of a download, some files may become corrupted/ incomplete. Therefore, when the lights do go off, my internet shuts down immediately and then even if the computer switches off, it would be after a certain interval from when the downloading stopped.
I keep my computers on 24/7 other than upgrades and patches. I just retired an 11 year old P4 2Ghz Williamette system this past week after the motherboard (Asus P4S333) finally died. The PATA hard drives (from 2000, 2002,& 2004), soundblaster sblive, PSU, and other hardware from that computer still works great, although it's hard to find a new motherboard with PCI slots and PATA. Not that it matters, but I don't plan on reusing these parts as they are old and slow compared to new hardware.
Anyhow, I don't think leaving it on overnight will hurt it.