Short answer is yes. the control computer controls all 3 power sources 12/120 and Propane (Assuming it's an RV type absorpton fridge)
now some of the 12 volt "Coolers" may not have a T-Stat (these are what I call -70 boxes.. Room temp - 70 degrees is about the best they can do and some only -40)
And last but not least they now make a line of 12/120 volt like my engel. Thermostat controlled.
But the answer to your question based on what I can infer from your question is YES there is a thermostat. Or as JRR Tolking would say "one Ring To Rule Them All" (Ring = Thermostat).