Freezer seems to be working ok, plenty of ice. Refrigerator is set at 37 but thermometer shows 57

The self defrost mechanism is not working. The evaporator is getting blocked with ice, an insulator, and that affects freezer as well as refrig temps. When you unplug unit the ice melts and it will work till the ice block returns.

You probably have one compressor that cools the freezer section and the refrigerator section. Usually the freezer gets cooled directly with the cooling coils. A fan blows cool air to the refrigerator section. The air flow to the refrigerator may be modulated with some time of "air door". What you have written says to me, is that the fans and air doors are working but there is enough cold for the refrigerator but not enough for the freezer.

Here is what I would do:

1. Put a thermometer in the refrigerator and in the freezer.
2. Be sure the coils underneath or behind the refrigerator are clean. If they are very dirty, clean them.
3. Keep the doors shut for at least 12 hours and then read the thermometers and write down the temperatures.
4. Freezer temperature
   1. If the freezer has started freezing again, you fixed it by cleaning the coils
   2. .If the freezer temperature is between 0 deg F and 32 deg F, consider putting the food in a cooler and packing in some dry ice to try and save it.
   3. If the freezer is warmer than 32 deg f, throw away the food.
   4. Doctors and hospitals are pretty expensive. I would throw away the food no matter what the thermometer read.
5. Look inside the freezer at the cooling coils. See if they are ice coated or not.
   1. If the freezer is above 0 deg F, and the coils are ice covered, the defrost control is not working. Unplug the refrigerator for 12 hours and let the ice melt. (Keep the doors shut.) Then, plug in the refrigerator for 12 hours and check the temperature like in step 3.
   2. If the freezer is above 0 deg F, and the coils are NOT ice covered, the compressor is not working.
      
6. Call the service technician. When she comes out show her the temperatures and tell her what you found out about the ice on the coils.

Good luck

It is likely to be either the circulation fan in the freezer or the defrost element. The cold air is blown from the freezer into the fridge if the fan doesn't work then no cold in fridge.Otherwise it could be a defrost problem, if the element doesn't work the rear fills up with ice and the air cant flow. Both are behind the rear panel of the freezer

Do you see any ice buildup inside the freezer? Look on the back panel

Clean the condenser grille, rear and under unit

There are many things that can go wrong with a Kenmore refrigerator ice maker. Your ice maker may be leaking. It may not make any ice at all, or the ice that comes out smells or has an odd appearance. The problem may have an easy solution, or it may require a technician's expertise. The troubleshooting tips in this article will minimally make you aware of what is likely the source of the problem. You may be able to fix the problem yourself and save a bundle.
When it Won't Make Ice
1 Get a thermometer and see how cold it is in there. If your freezer is fewer than 17 degrees F, it won't make ice. The freezer temperature setting may be too high or the thermometer is broken and not calibrated correctly. If adjusting the temperature fails to work, call a Kenmore technician.
2 Determine if your water fill spout in the freezer is plugged with ice. If so, no new ice can be made. Try clearing it out or melting the ice by running a hair dryer on it for a few minutes.
3 Turn your refrigerator around to look at the back side to see if water is getting to the water inlet valve behind the fridge. If the water is not properly connected, there's no water to make ice.
4 Use an ohm meter to test for coil continuity. If the ohm meter shows there is no continuity, then you will need to replace the water inlet valve.
Hope this may help you.
Have a good day: )

When it Won't Make Ice
1. Get a thermometer and see how cold it is in there. If your freezer is fewer than 17 degrees F, it won't make ice. The freezer temperature setting may be too high or the thermometer is broken and not calibrated correctly. If adjusting the temperature fails to work, call a Kenmore technician.
2. Determine if your water fill spout in the freezer is plugged with ice. If so, no new ice can be made. Try clearing it out or melting the ice by running a hair dryer on it for a few minutes.
3. Turn your refrigerator around to look at the back side to see if water is getting to the water inlet valve behind the fridge. If the water is not properly connected, there's no water to make ice.
4. Use an ohm meter to test for coil continuity. If the ohm meter shows there is no continuity, then you will need to replace the water inlet valve.

Have a good day : )

check freezer coil for ice, then defrost timer and then fan and switch fan

Sadly i would say the board is malfunctioning and needs replacement. There is nothing in the fridge/ freezer that if malfunctions can cause that.

you have either a Defrost heater / a defrost timer/ or a defrost bi-metal that is bad. if you post your model # i can look it up and show you how to set it into defrost to see if the heaters are ok
Since you replaced the timer already that leaves two things you need to check set it into defrost if you know how and remove the panel in the back wall of the freezer you should see the heater(s) are on if not check pwr 120vac at the heaters if 0 volts the bi-metal is bad