Many of us have a second refrigerator in an unheated location.

I've got both a refrigerator/freezer and a chest type freezer out in my 1600 sq/ ft. steel building. The chest freezer performs fine.
However, the refrigerator/freezer does not. When ambient temps approach freezing, the freezer portion seems to drift up to near freezing while the refrigerator temperatures remain cold.
Is this normal? I have the thermostats adjusted to the factory recommended settings. The freezer control is nothing more than a vane that directs refrigerated air to the freezer at the top.
Is there anything I can do to help keep the freezer section below freezing when ambient temps get near freezing? I have thought of moving all the freezer contents to the chest unit and using the refrigerator portion only. Is this my only alternative?
Thanks for the help.
