Thundar
Would it hurt a non-HD iMac if one watched a 1080p HD movie on an iMac? (He got it off YouTube.)
Squirrel
I'm not sure what you mean by "hurt". Playing a video back isn't going to bother the iMac one bit. The worst that could happen is that the iMac isn't powerful enough to decode the video and it won't look smooth.
In this case, HD only refers to the fact that the video has a high resolution (1920 x 1080 most likely). If your iMac's screen isn't this big, there's no reason to try playing a YouTube video at 1080p, as your screen has nowhere to put the extra video data (it will take all that data and shrink it to fit your screen, wasting CPU/GPU power).
Thundar
heat up the insides a lot kinda hurt
Squirrel
Okay, yeah, that's true. You can get some temperature monitors if you're that concerned. Or check your iMac's resolution and only get videos at the appropriate resolution. Or both!
Squishy Tia
Unless your iMac is thoroughly filled with dust bunnies, you shouldn't have much of a problem with HD content. Anything from the last four years should easily play HD content, and if you iMac has a MiniDisplayPort on the chassis to allow connecting an external display, you'd find that connecting such a monitor/TV would properly display HD content.
It might not play it smoothly, as Squirrel noted, but it shouldn't damage your system either. HD playback takes less GPU than World of Warcraft, which already is CPU bound.
You'll be fine.