markh interesting concept.
The temperature sensor on the beer chiller, is actually surrounded by the cooling element.
You are right as the air temp drops, the air has less ability to hold water. That is why all fridges are like dehumidifiers.
Obviously as the pump pushes the refrigerants through the cooler element, the cooler element will have a lower temp than the surrounding air therefore condensing the water from lower temperature air on it. As cold air drops below the warmer air and falls into the well of the chiller would this not act as an air circulating event. I believe it does.
I was thinking about using a peltier device but as they normally will only give a temp of about 20 degrees below ambient. I thought this unacceptable especially in the really hot weather.
I look forward to hearing the results of your experiments. I would also be happy to hear if you disagree with my logic in this post.