Furnace should not create moisture inside. All combustion products are sent out exhaust vent, however just living breathing and being in a small closed up space causes humidity, that coupled with cold walls creates condensation. Try opening one or two windows a crack. Also if you had condensation on walls, you may have some under bed. The moisture from your body goes through mattress and will condense on the cold bed frame. After camping in cold conditions, I always prop up mattress to dry out for a few days. You can try a dehumidifier, but you need to be aware of the current load especially if you are running electric heat.
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