I have a small rv 17 feet by 8.5 feet, some nights I will need to run my electric heater for a few hours.?

I have 6 deep cycle marine batteries permanently connected to a 120 watt solar panel with a charge controller and power inverter. I don't have much running on this system other than LED lighting and thats few lights. I also have a PC that i use for a few hours some days, and a small flat panel TV used for 1-2 hours a day. Some nights I know I will need to run my little electric heater just to warm me up while I sleep or fall asleep. I don't plan to leave it on longer than 4 hours at a time at night mostly. I have noticed that my batteries recharge very fast and I don't think this would drain them completely if I use the heater responsibly. What can you guys suggest, I'm not to eager to get more propane burning, since I already have a propane stove. I noticed that it takes one 1pound propane tank every 3-4 hours to run a propane heater so thats not a cheap option. Can someone share some knowledge pls.