The low 30s at night isn't cold enough to bother your coach. Low 30s could make some ice on/in an exterior water hose for a few hours, but would not bother your coach's interior, be it living area or basement. That being said, if your coach will be plugged in with the electric water heater engaged and with the inverter on, then your basement will be heated. Your inverter puts out quite a bit of heat when operating, and your basement furnace is always on. If the basement furnace's thermostat sees a temperature of 45F (?) or lower, then the basement furnace will actuate. Interestingly, on cold nights I have seen my basement temperature climb to above 80F. I don't understand why it would get that warm. I would have thought the basement furnace's thermostat would shut it off and not make it that warm.
My AquaHot is the AHE-100-02S and I am sure your coach is designed differently, but not much differently.