Well, I have the exact same machine sitting under my desk right now, and it's been on in a cool (cold, really) room, running at near idle for about an hour. The heatsink is definitely hot to the touch, and although I could probably keep my hand on it, it wouldn't be comfortable near the middle. I expect it would be hotter if the room was warmer, or I'd been running the computer harder (I think; not sure if the G4 uses more power when it's doing something).
I doubt your heatsink temperature is abnormal--they do tend to get VERY hot these days--you should feel how much heat comes out of the back of a G5, and I've seen videos of AMD Althlon chips literally burning themselves when the heatsink is removed. Downloading a temperature check app will tell you what the processor is actually registering, though, if you're suspicious.
The freezing problems you're having aren't normal (unless you're on OS9, in which case one bad app can easily cause crashes like that). They could indeed be due to heat, but bad RAM is the most likely cause, and other types of hardware failure (motherboard glitch, flaky hard drive) are also a whole lot more likely than overheating, unless your computer has very restricted airflow or is in a very hot room.
If you added any extra RAM when you got the computer, I'd try pulling that out and seeing if it works better. Good luck.