Using a dimmer sounds like an easy answer to the heating element problem. There are some things to think about before using one. First an understanding of how a dimmer works is in order. This explanation is far from complete but should be good enough for now. A dimmer chops up the power 120 times a second. With some bulbs you can hear them vibrate as the power goes on and off. To change the brightness of a light bulb the chopped power is turned on and off for various lengths of time. To make it bright the power is on most of the time. To make it half bright the power is only on about half the time. To make it dim the power is off most of the time. This works great for light bulbs and will work for the heating element in the refrigerator.
The problems come in when you try to run other equipment on this type of power. One problem is that it generates a lot of electrical noise that you can hear in an AM radio. Transformers and power supplies will not work correctly and may overheat and burn out. Relays will not work sometimes. The biggest problem comes from measuring the voltage. Most voltmeters will not read the correct voltage when measuring this type of voltage. Some special meters will. If you cannot measure the voltage you cannot set it to the value you want to produce the desired power level for the heating element.
For the above reasons I would not try to use a dimmer for this application.
