If so, doesn't that imply that there is no change in temperature that could possibly decrease the humidity of such a system?[\QUOTE]
Well first, just to be sure, I think you are talking about absolute humidity, right? Absolute humidity is the amount of water vapor per unit volume. In your closed system the amount of water is fixed, so the absolute humidity will change if the volume changes or some water condenses out. As I said the volume could change lowering the humidity. An example would be the isobaric heating you already indicated would lower the humidity. So for arguments sake let's say we are talking about a fixed volume, in which case, ok, heating it won't change the humidity. However cooling it certainly can change the humidity. Your premise ("completely filled with humid air") isn't completely clear, but let's take that to mean 100% relative humidity. This would mean that any amount of cooling will condense water and lower the humidity. (Water in droplets on the wall don't count in the definition of humidity). We don't have to assume 100% relative humidity. How much water vapor just changes at what temperature the water starts condensing out.
G Cooke said:
Doesn't that then imply that there is no way to decrease the humidity of such a system? Of course, no molecules are entering or leaving, and the pressure cannot decrease since it starts with the volume completely filled, right? So I think that exhausts everything.
The pressure can and will decrease if you lower the temperature at constant volume. (Ideal gas law: P V = n R T). Water will condense out if you lower the temperature enough changing the humidity.