I also have an ARE MX series cap, w/3 win-doors.
If you have a properly sized inverter set up, dual batteries, decent alternator & only use it while engine is running, you could run a small elec heater. Or if you had a small generator, you could use it all night. We use this one for our camper: (
http://www.pattonproducts.com/ ) -the red one, Patton PUH4842M-RM. It will heat our entire 18' camper, on low, to the point that you will be too hot, in just a few hrs when you can see your breath outside. Our camper is insulated though.......but it's a camper, so no where near house insulation standards. I would just be leary of combustion inside a small space. Hard to modulate a wood stove inside such a small space as well, I would suspect. Plus, you want to sleep. The elec one is either on or off. It has a fan only, low & Hi heat settings. It also has an adjustable t-stat. It uses 1500 watts on Hi & between 700 & 1300 (not really sure) watts on Low. It also has a safety tip over shut off & an overheat shut off. Also has a nice cord wrap on back. We liked it so much, we bought a second one.
So, can you use a wood stove inside you cap ? Yes, you can. Would I do it ? No. My cap cost $3650 total. I would not want to take a chance ruining it with excess heat. I would use our elec one in a heartbeat though, inside the cap.