Thank you for the detailed information. I am now able to reproduce this on our web dashboard with my own pi's and DS18B20 sensors. It looks to me like its not related specifically to the Fahrenheit vs Celsius units setting, but just that any setting change on that widget is not saveable. On my end, I can't even rename the widget, the Save button just isn't behaving for this sensor.
We're investigating internally and I'll update as soon as I know more.