The majority of trailers are drafty/poorly insulated and as you have discovered the furnace may cook you when it is on and then you will immediately feel the chill when it shuts off. We use two oil filled heaters and these put out a steady flow of heat even as the element turns off and on. With them placed near windows or outside walls they do a reasonable job of uniform heat without a fan constantly running.
However, I do not depend on the cheap 'thermostat' which really just sets the power level, not really the temperature. Instead I use LUX Win100 controllers with their own temp. sensor and the heater plugs into the controller. The advantage is that power output will actually increase at lower night temps and it will drop to zero during the day without my touching it. On days with big temp swings, I can leave the trailer at 7am with the heaters still running and return at 4pm with the heaters off and the A/C running.
I have camped for several days with temps in the 20's, the propane furnace shut off, so no heat to the basement or holding tanks, yet the fresh water tank, pickup tube and water lines did not freeze.
