Thermostats can be mounted in places that don't represent the temp very well, they can be in a situation where they might be overly influenced by the outside temp., through a cold wall.
They can also not be tuned very well.
Take the cover off the mechanical thermostat and make sure it is not getting stuck, that the small wires inside are not affecting it's operation as it moves based on temp. They are very sensitive to this.
There is an anticipator in every mechanical thermostat I've seen. This is an adjustment that can be made that cycles the heater as it is doing it's job, so that is doesn't overshoot. Some of the current that the thermostat is controlling is used to heat the bimetal coil that rotates to make or break the switch. Adjust this to where the system cycles more, and it will overshoot less. They usually say "longer" and have an arrow. Adjust it toward shorter and see if it helps.
Switching to a digital thermostat is fine too, but in a small environment like a small fiberglass tailer, the thermostat response may be so slow that the trailer is already overheated by the time the thermostat recognizes the temp, and shuts off.
For the trailer, I like a simple mechanical thermostat, with a thermometer on it. It should have an on-off switch, or a separate wall switch that controls it. Don't worry too much about the actual numbers on it's scale, just find a setting that is the best compromise. A programmable one is OK too, if you don't want to keep waking up to the noise during the night. Set it to come on when you wake up.
All thermostats have a differential between their "off" and "on" temp. This is usually about 3-5 degrees, and is not the reason for overheating. Older mechanical thermostats had a mercury switch that would last a lifetime and was very sensitive. These are no longer sold
, but are very good. They must have an off switch too, or they will be cycling as you drive.
Bottom line: Small trailers are hard to manage the heat in. The thermostat must be in the right location. It must be a sensitive type. The anticipator function can help stabilize it and reduce overheating. Even if the heat seems to overshoot, let it settle in and stabilize, before judging it too harshly. On cold nights, it should begin to cycle regularly and run for about 10-30% of the time, on a repeating cycle.
Here is a link that might be useful: