Hello MontyJ,
I have a different experience with using air pumps and their relation to water temps than stan. You can run your own tests, and your experience may vary from either of ours. For me I have two water culture systems running outside in 102 to 110 temps right now, and both remain cool. I do add ice to them daily, but not because of the air pumps. Regardless If I had the air pumps running or not, the water temps would get high without adding ice to bring the temps back down.
I know theatrically it stands to reason that pumping warm air bubbles into cool water should warm it up. But I haven't found it to work that way in the tests I've done. Years back I thought using this principal I could cool a
nutrient solution by pumping cool air through the air
pump. I took the air pump and placed it in the freezer, and closed the door with the plug and air line running out. I took a container with about one gallon of water in it and took the water temp before the test. Then placed the air stone in the container and plugged it in. I let it run like that for over an hour and tested the water temp. The water temp was exactly the same after, as it was to start with. There was no temp change at all.
Also just to let you know, the saturation point of dissolved oxygen levels in water is directly related to temperature. The higher the temperature, the lower the dissolved oxygen level. Thus the quicker it will be depleted by the plants.