Well, in the first days I had the same impression: It seemed to me that Aperture (3.0.3) was the trigger of sudden shutdowns. Heavy computation after migrating my image database to the iMac were interrupted a lot.
Then, the same happened with iTunes after migration of the data. In both cases big parts of the data are on a QNAP NAS, so I suspected that combination not to be fitting.
In the end it turned out for me that sudden shutdowns also occurred using several other software (Mail, Safari, even Finder some times). The conditions varied from high cpu load to nearly idling, from over 60 degrees Celsius (that's 140 F) down to 28 C (82 F), with a lot of apps running at the same time as well as only one app open.
So, I am not able describe any condition to be typical for sudden shutdowns.
After biting the bullet and reducing the RAM to 12 GB one week ago I didn't experience any shutdowns at all. Though I hate to not being able to use full 16 GB of RAM, it seems to me the best deal between effort and benefit.