Thanks for making me sound stupid.
Yes, I've noticed there's a lot of that on this forum. Some might say too much.
A cooler mac is a longer lived mac.
Any G5 is going to put out a lot of heat due to their nature. The G5 uses a special Torx screw driver that has a long shaft to remove the heat sinks, from there a standard computer repair tool set will handle the job. I do not recommend messing with removing the logic board and what not to change the U3 pads/paste unless you really know what you are doing. As for adding more fans, there is very little room in the case and any fans you do add would be noisy due to the lack of computer controlled cooling at that point.
You are right, the case is huge, yet space is limited inside. If there is a mount/bracket for extra HD/SSD's, behind the front mesh beside the ram sticks, this compromises air flow. Not a big issue where I live, but in summertime Ohio it might make a big difference.
If it's not there, it looks to me like a slim 140mm fan could be slid in and fixed to the front mesh to increase air speed. Might be worth having a speed regulator in line, to fine tune between too hot and too noisy.
You could try a PCI fan or 2, they move heat out of the case nicely.
Have you considered externally mounted fans? You could fit two 150mm fans to the front of the case pretty easily, I like the Delta AFC1512DG, good air flow, good static pressure, noisy at full speed, I'd deffo fit an inline speed control to fine tune between too noisy and too hot.
If you're brave and don't mind Steve Jobs turning in his grave, you could remove a chunk of that front mesh and either fit a wire type finger guard, or even leave an empty hole (I'd fit the finger guard) this should give a small improvement on the mac's already pretty good air flow.
If you have a lottery win burning a hole in your mink trimmed silk and cashmere pockets, or you've simply run out of space to stack all those bundles of $1000 bills, you could have a liquid nitrogen cooling system and your very own cryogenic cooling plant. In the real world there's water cooling, but it carries risks, I personally no longer recommend this option (after a long and very serious chat with a mate who mostly tests high end PCB's for a living).
OK, so that was about getting the heat out of the case, here are a few things that might reduce the heat.
Running in Reduced mode, as suggested by Dronecatcher, is a good idea.
Have you considered down clocking the graphics card and/or swapping in a cooler one?
How many HD's do you have? What's the over all capacity? Can you fit fewer and/or cooler running drives?
I'm not sure I'd actually recommend it, but only having two 256mb ram sticks should lower overall temp a little.
Are there any PCI cards fitted that aren't actually in use, they kick out heat (some more than others).
Lastly and definitely most sucky, you could swap it for a 1.6 single core machine, it runs the coolest. I think you might need to be very desperate to want to try this option