I assume this is what is known as a "dorm room" refrigerator. And it has a compressor with an induction motor. I looked up what your power is in Chile, 50Hz, 220V for low volt single phase.
You can make your own thermostat, or you could purchase a simple one off eBay, like this
http://www.ebay.com/itm/All-Purpose-Temperature-Controller-STC-1000-Thermostat-Aquarium-NTC-sensor-220V-/251312628190?pt=LH_DefaultDomain_0&hash=item3a836661deMy search was ("STC1000", "STC 1000") (220v, 230v, 240v)
There are others that have PID control, but I purchased one, that was impossible to use, as the instructions were incomplete (not fully translated). The above one is very easy to use. It also has a built in delay timer for use with refrigeration so the power stays off for a programmable number of minutes so the pressure in the system can equalize and the motor can start with no load.
A refrigerator, does not need any sort of PID control, just a bang-bang (on or off) controller.
The only issue with the above thermostat, is it has a relay that most likely can not be used directly to switch power to your compressor motor. It does say 10amp@250V, but it does not have a motor rating power stated, it may work with out problems. If not, either a larger relay with contacts that support the motor current, or a solid state relay should be used.
You indicated that the PTC of your existing released gas when you opened it. Was there a copper tube connecting it to the electrical switch? I'm guessing this had a saturated refrigerant type working fluid.
Also did you mean "highest" temperature setting (versus lowest), as it never shut off, causing the temperature to drop below freezing of your cola. The release of this working fluid would result in the thermostat never shutting the compressor off.
Lots of nice lab work and measurements. Good luck.