The commonly referred to "slide thingies" suck! I had a problem with the old Dometic Fridge freezing everything...including the beer, the pop didn't like it and the wife didn't like the clean up (I had to thaw the beer so I couldn't help).
Anyway, I found a product called "Snip the Tip" at snipthetip.com I am not advertising but for about 30 bucks you get a real thermostat the size of your thumbnail. It uses the wires going into the slide thingy. Turn off the power and simply snip of the tip, separate the 2 tiny and I mean tiny wires and connect to the new thermostat. Restore the power and set the temperature you want. Now your fridge is thermostat controlled! Takes about 5-7 min for the whole process and works!
Just bought a new trailer and am already ordering my snip the tip kit!
Happy Camping ya'll!