Most of the replacement home thermostats are for 24 volt systems. I have one of those and it works fine on 12 volts.
I would pull the thermostat off the wall and disconnect the B or BW wire (probably red) and see if the fan stops running.
If you wan to see if the 12v is working you can always run a set of jumper cables from your truck battery to the trailer battery cables. Remember though that on trailers usually the white wire is ground and black or red is positive. Verify the ceiling lights work on 12 volts and then see if the heater sill come on.