I agree, gas fumes can be very toxic to plants.
and you would probably get a wild swing in temperatures with that method.
from oven to deep freeze.
You'll probably only need the warmth of a single light bulb at about 30-50 watts turned on during the night, or very cold days to do the job.
Installing it in a large tin can, wrapped in fiber glass insulation with metal fly screen over the opening would keep it from catching your straw, leaves etc. on fire. in a small, enclosed environment, a single light bulb could keep the insulated space at, or just above freezing.
Instead of mothballs, (which can also be toxic to some plants), i'd place an unopened box of Decon near the trunk, the mice will chew open the box when they get hungry. If no mice get in, the box is good to go for next year.
Using plastic for insulation during the winter is never recommended, it traps too much moisture, which then freezes, and kills live plant tissues.
The idea is to keep out the cold, without holding in moisture that will freeze, and damage your plants.