as from subject, I'm really looking for a log file about CCleaner activity when it's run as scheduled task: there isn't any track of CCleaner activity after it's execution except the task status (0x0) indicating a correct or not execution.
But I would like to know details of what it has done (of course launching normally it works but this is not my target).
If you use the CCleaner /AUTO switch as detailed in the Beginner's Guide you should first run CCleaner normally to configure the programs you want it to clean in the large cleaner button.
It only cleans programs that are in the Cleaner button when using /AUTO, it doesn't clean the registry as there's no functionality to automatically run the registry cleaner.