GE Wine Cooler iceing

I noticed that ice was forming in the wine cooler compartment where the coolant lines enter / attach inside the box. I noticed that the cooler seems to run constantly but I am not sure if just the fan or the fan and the compressor are both running. It will turn off if I lower the temp but the ice has started forming after it has been defrosted. I cleaned the door seal and it appears to be in good condition. I do not have a wiring diagram to see if the fan is suppose to be on all the time. I suspect that the thermostat could be bad but it is rather expensive and want to check the problem out to be sure. Any ideas or information you could provide would be much appreciated! Also if you could point me to a wiring diagram that would be great also. Thank you!

You have refrigeration problems assuming the compressor is running and you get little cooling.

Thanks for the reply. I finally got a chance to look at the wine cooler. I turned the temp all the way up and let it run for about 2 hours. The temperature dropped from 71 to 52 degrees. I then reduced the temperature setting to it’s lowest level but the compressor did not shut off. It seems like the compressor is running and cooling ok but it never shuts off. I am thinking that the problem is probably the thermostat because I think the compressor should have turned off when I reduced the temp to the low setting. Does this make sense? If not, and the compressor was the problem, would it be cooling at all?

Thanks for your help!!