Possible to run heat at night without killing your batteries

I have no idea of something else is running them down. At night all I know that is running is the Furnace. All lights out etc. Also I have no idea about solar stuff. What's a decent solar system to look into? I'm at work for a week so not gonna be able to check battery voltage or anything for awhile. Will probably just replace batteries and start over since this is new Coach for us and have no idea how it was taken care of before we took possession of it on Friday..