Today I got some news from the computer repair shop.
Apparently the problem has nothing to do with overheating. It seems that the first series of iMac G5 used a bad batch of capacitors on its circuit boards (I think that sensors for the space shuttle fuel tank were plagued by a similar problem recently!) and that they burn up after a while. Apple has acknowledge the problem and extended the warranty of the flawed models (see the Repair Extension Program page). So as soon as they received the needed parts the repair shop will replace the logic board of my iMac G5 (hopefully before the end of the week) and I will be back in business with a FAST computer (switching back to a G3/G4 made me realized how fast the G5 is!). Let's see if Apple hold to their reputable customer service.
I have therefore regained confidence in my beautiful iMac G5 and will stick with it for a while. Probably until we see what those new Intel Mac that Apple is planning to release are capable of.