Thanks to all for your help!

I sent it to apple and they replaced the logic board without any charges.

First of all it doesn't sleep randomly anymore so I am able to work normally without interruptions and secondly I don't feel like working in front of a blender anymore.

Happily I paid the AppleCare protection plan, so hopefully I don't have any problems with the iMac at least until all macs are built with an Intel processor (end of 2007?).

P