Tues and Wed night could freeze some lines if they're exposed to ambient. If you hadn't just bought the camper, I'd suggest you may know where the water lines are and it would likely be fine with the heat on. Considering it has tank heater(s), is it marketed as 4 season capable?
It's not the couple gallons in the tanks you need to be concerned about anyway until it freezes longer and they have more water in them, it's the lines.
If you have the time, no time like the present to figure out where the water lines run and if they are insulated/see heat from the furnace.
Good time to figure it out, if you camp in the cold weather anyway, or could be camping in cold weather.
Have fun!