They operate silently, the cooling process consists of a small flame or the electric heating element heating a water/ammonia mixture.
The ammonia evaporates from the water and convection carries it upwards to the cooling plate in the freezer. As it condenses back to liquid it absorbs the freezer heat, cooling it down. Then it flows downward towards the bottom of the fridge, shedding more heat through the cooling coils on the back of the refrigerator.
When it gets to the bottom, it re-combines with the water and flows back to the boiler to repeat the process.
The freezer has to cool first, after it's down to the proper temperature the excess coolant flows through the refrigerator section.
Make sure the doors are sealing properly and there aren't air leaks into the refrigerator or freezer. Remember, if the freezer takes more cooling to maintain it's temperature there won't be as much cooling left over for the refrigerator.
Take a dollar bill, close the door on it at several locations and make sure it drags as you pull it out. If there's no drag the door seal isn't closing firmly and you have an air leak.
In hot weather, sometimes you can boost the cooling by directing a fan upwards behind the refrigerator to help the waste heat exit through the roof. Normally the airflow is taken care of by a chimney effect, the hot coils heat the air around them and convection makes the hot air rise out the top vent while cooler air replaces it from below. As the outside temperature warms up, there is less difference between the coil temperature and the outside temperature so the convection flow breaks down.
It doesn't take much, a 12 volt muffin fan works well. Or for a trial, you can get a small 120 volt clip-on fan for about $10 at Walmart, clip it to the edge of the lower vent and let it blow upwards on low speed.