If you are renting a refrigerated truck, it gives you the opportunity to transport food and other goods that require a specific temperature. However, it does not necessarily mean that you should transport a full refrigerator inside that truck.
A full fridge can pose an issue, as it may leak water through the freezer section if it is taken off its power source for a few hours. We recommend inquiring with a professional about the best way to transport the model of fridge you own.