I think we may have to Taboo the word "cold" in this posting. As I understand it, an object is colder than another if it has a lower temperature than another (in other words, the average kinetic energy of its molecules is lower than those of another object). Therefore, knowing the exact position and velocity of all the (classical) molecules in an ideal gas doesn't make the gas "colder" until you actually DO use Maxwell's Demon on it. Saying that an object that you know enough about to use Maxwell's Demon on is "colder" than another conflicts with my understanding of the word. It's not actually colder, it's only "potentially colder" (by analogy to potential energy), if that makes any sense.

Yes, we're arguing about words, but that's because we're getting confused. :(