Temperature Cycles Inconsistently in Freezer and Fridge

Based on the information you provided, it sounds like your Kenmore refrigerator is operating normally.
Most modern refrigerators are designed to cycle on and off in order to maintain the temperature inside the fridge and freezer compartments. During the "on" cycle, the compressor runs and cools the refrigerant, which in turn cools the air inside the fridge and freezer. During the "off" cycle, the compressor stops running and the refrigerant flows back to the compressor to prepare for the next cycle.
The length of the on and off cycles can vary depending on factors such as the ambient temperature in the room, the amount of food inside the fridge, and how often the doors are opened. However, it's normal for a refrigerator to cycle on for around 10-15 minutes and then off for around 20-30 minutes.
If the temperature inside the fridge and freezer compartments is staying at the correct levels, then there is likely no cause for concern. However, if you notice any unusual sounds, odors, or fluctuations in temperature, it may be worth having a professional technician inspect the refrigerator to ensure it's functioning properly.

There is a balance between the freezer and fridge. Reduce the freezer temp and see what the fridge temp does. By reduce I
mean make the freezer warmer. If it is set too cold the fridge gets colder.

Possible faulty freezer fan motor. Dirty condenser. Faulty control board.

you need a new thermostat e z to put on it takes a phillips screw driver the t.stat is hooked right to the knob that you turn to adjust the temp

Check the door gaskets, condenser fan, refrigerator fan and the freezer fan. That should narrow down the problem.

I need you to confirm that your model number is ZICS360NR and I will help you, Sea Breeze

The freezer is usually cooled by the compressor, the fridge is then cooled by an evaporator fan motor ($30). If this fan seizes or slows down then the fridge warms up (it sometimes starts squealing before this happens). The fan may spin, but it if goes too slowly, then it would blow enough cool air into the fridge, especially if it is opened quite frequently.

If you think it is the evaporator fan motor:
Check to be sure you can get a replacement fan first, they last about 4 - 5 years. Can get from a parts supplier or electric motor company.
UNPLUG fridge. Located usually in top of freezer behind a vented cover plate. Remove cover, remove screws holding fan in, may have to cut wires. Replace with new motor, make sure the fan pushes air into the freezer area and doesn't spin backward drawing air from the freezer area.

The fridge gets its cold air from the freezer through a vent(damper) between the freezer and fridge.The fan in the freezer blows air through it. Make sure this fan is running. You may have to hold the door switch in for it to run. There is a flap you adjust with the fridge temp. control. Make sure it's opening and closing when you adjust the fridge temp.
The problem could be the electronic control if you have one or the mechanical linkages.

Turns out the problem was because we didn't shut the freezer door tightly. The temperature re4set itself in about three hours. All OK and no expense :-)

In most refrigerator freezers, the refrigerator gets its cold from the freezer. The evaporator fan circulates air over the coils in the freezer and cold air circulates into the refrigerator through vents. If the vents are blocked or closed, then the fridge will not get cold enough but the freezer will. If neither is cold enough, then the number of possibilities increases.
Lowering the freezer temperature will increase the cooling cycle activity. Setting the refrigerator temperature may have little affect on the cooling cycles because it simply changes the vent opening size. Decreasing the fridge temperature opens the vents more and increases air circulation from the freezer.
The temperature can be adjusted using the controls found inside the refrigerator or freezer. The ideal freezer temperature is about 0 to 5 degrees (F) and about 38 degrees (F) for the fridge.
Measure the temperature by placing a cup of water with a cooking thermometer into the refrigerator for about 2 hours or more. To test the freezer, substitute alcohol or cooking oil.