The only way for water to be warmer than the ambient air temps is if you add heat. The most likely way for you to be adding heat is through the pump. Normally your water temps will run 10 degrees cooler than the air.
What happens when you run your pump for 15 minutes straight is it starts to heat the water slowly. Water conducts heat very well and retains it even longer. What you really need is a 1-4 minute timer. One minute on, four minutes off. Then the water never has a chance to heat up. What little heat created is lost naturally to evaporation cooling and the waterfall effect. It's a lot cheaper to buy a new timer than a new chiller. If that doesn't work I'd be like, WTF? The only other heat source is your lights...
Here's what I've learned from my experiments with Aero/DWC. My first designs actually worked better than my last designs. It works better if the roots never hang in the water. Then you don't have to deal with air stones. What I did was take one 2 gallon bucket and put it in a 20 gallon storage bin. Then I bought one of those lids that have the net pot built in. I had a pump in the bottom res that pumped up to sprayers in the bucket. The water just drained through the holes in the bucket. The roots just all hung down and stayed in the bucket.
Another design I tried used air stones with the netpot and roots hanging in the water just like a traditional DWC system. Of course whenever you have roots in water you need lots of air to keep from drowning the plant. That means more air stones... which means more heat... Then you start needing chillers or ice bottles, etc..
My current veg unit uses 2 - 27 gallon strong boxes, one stacked on top of the other. The pump is in the bottom box and plants are in the top box. I have a simple EZ-Clone sprayer setup and the plants love it. I could easily grow just one big plant if I had the room, which I do...