Using a temperature relay as a fridge temperature control thermostat
I see no reason why a device such as the Siemens 3RS1 could not be adapted to control a refrigerator.  I'm assuming you have one on hand as the price of one of these is close to the $150 that you are saying is out of the question.

Keep in mind that this device has no built-in thermometer, so you'll need to add an appropriate one of your own.  Also be aware of the output capacity so that you don't damage it by switching the compressor on and off.