My friend Kyle came over last night, and I showed him my project. One idea we had was to just make adjustments more slowly. Implementing that actually made the device work exactly right, except that it took forever to happen. Setting the delay to 2 seconds allowed the sensor to catch up with the water temperature and stop adjusting when it reached the desired temperature. So that's great, except it takes like 15-20 seconds to adjust, and by that time you'd just be angrily doing it yourself.
A possible solution would be to guess how much to adjust it. When the temperature changes by 5 degrees, it'll rotate X amount and then wait a few seconds to see if it was correct.
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