I know from experience if you block the bottom intake vents on a VIC 20, so it can't convect properly, it will eventually start acting funky.
On a related note, I understand the 64's original power bricks are considered timebombs, they might also not appreciate being left on for weeks at a time.
Yes. These early computers found their way into various embedded control applications too, and I suspect there's quite a few C64s still in operation that way; they would've been replaced long ago if they weren't stable. An article occasionally appears when someone discovers this:
If you block all air circulation, sure you might eventually end up with problems, but it takes quite a bit.
Now the 64C was released in 1986, four years after the 64 and its faulty power supplies came out. I don't know whether Commodore had decisively fixed the flawed PSUs by that time, but I know for sure that my second PSU lasted for the lifetime of that device too.