OK, when the coolant reaches operating temp its then flows into the radiator via the stat. Then the colder coolant from the radiator then flows into the engine to keep things at a constant balance. Without that there will be over heating. The radiator is there to cool, so when the temp of the coolant in the motor reaches the temp of the stat, it opens and the cycle begins to prevent overheating.
I don't see how what I said before is backwards, it was just a basic explination.
We were tying to explain why a colder stat would cause the motor to run warmer, and how a warmer stat can actually cool more efficiently.