I have the Dometic and single zone LCD t-stat also...I have experience the same thing with my Bedroom AC fan on Low over night, running fan on HI I've had no issues.
I don't know if the freeze sensor shuts it off or what, but on high it doesn't experience this issues...Dometic needs to improve this thermostat....it has other issues also, such as the fan switching from hi to lo and back to high as you initially cool the RV in Auto mode...this can also be fixed by using HI until the temp set point is reached.