Thanks for the replies. Well it's a Coleman analog slide type control. The workings inside are electronic (thermistor or varistor type sensor) as apposed to the mercury bulb (don't think you can get those any more) but not a "LCD" read out so I'm going to call it analog.
It is digital in some respects as the temp sensor is completely electronic, but because it has a slider control on it I think most people call it analog.
Hears what I found, and totally by accident too.
I had pulled the stereo out to try and find out if there was a sub woofer connection. There was and it wasn't connected to anything.
(Another modification ..... See 2306 sub woofer addition ......another post)
I found that the cavity the stereo was mounted in, and the thermostat mounted on was CRAZY HOT inside. This is because it shares a wall with the refrigerator. The heating assembled for the refrigerator is closest to that wall. Further investigations found that there is a wire hole made at the factory about half way up in the cavity where some 12 volt wiring enters into that cavity. No one ever plugged the hole with insulation. This lets heat/cold into that cavity from the refrigerator compartment.
I actually found that bug a boo on another trek inside the cavity when I had the stereo pulled out and the "fantastic bathroom fan" on. This was creating a negative pressure condition in the camper. You could feel the air zooming through that hole.
I plugged the hole with a wad of fiberglass insulation. I knew that the heat generated by the operation of the refrigerator "was tricking" the thermostat into thinking it was above 80 degrees in the camper. This is why it got to be freezing in the camper with the air conditioning on. The stat thought it was still above 80.
Now that it's winterized, I tried it with the heat before making my modification. Took several hours but when the thermostat was set at 70, the inside temperature was now above 80. Sure enough, it was getting hotter inside the camper than the stat setting. Thought I'd get heat stroke before it would shut off.
With no air flow through the cavity and being heated or cooled by either the outdoor ambient temperature (winter) or the operating temperature from the refrigerator (summer) it was fooling the thermostat.
My solution was rather than buy a different thermostat, relocate it or the like, I decided to see how it would work if the air temperature around it was correct. Sure enough, it worked, so I made the following modification.
I installed two computer type type 40 Cfm 12 Volt fans on the side wall of the cavity. The one at the top pulls air out while the one at the bottom pushes air in. I wired them in series so each fan is running on 6 volts. This slows the fans to 1/2 speed and makes the operating noise so low you can't even here them run. The current draw is so low that I just wired them to "stay on" continuously as the camper is plugged into shore power all winter.
Now the air behind the thermostat is the same temperature as in the camper.
WOW....... What a difference. The heat cycles properly and I used a digital thermometer to check the accuracy of the temperature in the camper to what the slide bar on the thermostat was set at. There identical!
The moral of the story is that the thermostat is not faulty but the mounting location was not engineered correctly.
The fans probably cost less than a new thermostat, but probably took longer to install to be cosmetically perfect.
I am planning on upgrading my stereo anyway with the addition of a audio power amplifier in that cavity so "for my purposes" the fans will serve a dual purpose.
I will post photos if anyone is interested.