I too have 3/4 foamboard sandwiched between 1/8 inch ply on each side. totaling 1 inch thick walls.
I have a vent free blue flame heater, its burning about 3to 4 gallons of propane a week and that puts 3to 4 gallons of water vapor in the air a week as well.
I now see that I need to get a vented heater.
http://www.ducktec.com/itmidx14.htm
their smaller unit here looks to be perfect!
the only place ice is building up is the bottom few inches of the aluminum door frame inside. I chip it off once daily.