I wouldn't use anti freeze at this point either. And you can make an argument either way as to whether to run a thermostat or not. I usually do, but you have to keep a closer eye on the temp as you are restricting the water flow even when the 'stat is open. But I don't use distilled water. At the risk of starting a debate on this minor point, here is an interesting article from Rislone as to why I don't:

https://rislone.com/blog/cooling/why-you-should-never-use-distilled-water-in-your-cooling-system