If you have the money, the iMac is a far better machine. So as far as that, it's completely up to you and your finances.
This machine is for a very small market. Apple knows this. It's for those that want/need a cheap, headless mac. Someone that already has monitors/keyboards laying around and want to "try" Mac OS X. It's also for those that have the missing equipment pieces (keyboard/monitor) and are looking to upgrade old macs on the cheap. For that this is a GREAT machine.
With that said, this machine will play Warcraft III and Civilization just fine. You won't be able to have all of the graphics settings at maximum, but yes, they will play just fine. The problem with your logic is that you seem to suggest that Warcraft III (and the like) will be the only games you will ever want to play. If that's the case, then fine. BUT, if you plan on playing new games that are increasingly more demanding, then the G4/32MB graphics card will be more and more lacking.
Heating? If you know of a computer that will overheat due to being on too long, then let me know. The manufacturers should be dealt with severelyi. I never turn my machines off. Never.
The G5 is faster than the G4. Just look at the bus speeds and MHz. It's proportional. And you can expect about a 1.7x actual speed of x86 chips MHz ratings. So again, it's up to you.
Hope this helps.