I read in all the literature that the climate control is supposed to change when the top is put down to maintain a "constant temperature". I know this is not really possible, but I would suspect it would at least redirect the air lower. I don't notice any change to the air conditioner when the top goes down. However, I do notice a big change in the stereo sound.

Is something really supposed to happen to climate control when the top is brought down?

More warm or cool air is directed to lap and footwell areas, instead of the upper vents, which would be mostly wasted blowing up high.
If you have your normal vents set to blow into footwell you will not notice much of a difference, however if you have the upper level vents selected, then that air will be redirected.

Net effect is to have a very comfortable interior with the top down, without lots of fan noise.

Just came back from a beach run. Had air on with Sun up, and warm air blowing when it cooled off. Fantastic!

I didn't seem to notice the redirection of air. I'll check it out again. Thanks for the reply!