Why does my refrigerator not get cold

Hi, With the limited information you supplied I’m going to assume there is an ice build up at the rear of the freezer. Your problem is going to be with your defrost system. I will also assume you have the ability to repair this yourself.
This is going to be one of three problems with your refrigerator, 1st thing to do is remove shelf’s and panel in the back of the Freezer. You may see ice build up on the evaporator, don't worry get a hair dryer and melt the ice.
Next locate the wires for the defrost heater and using a multi-meter/ohms meter test the heater for continuity (it should read infinite) if the defrost heater is bad replace it.
This is what a typical defrost heater looks like:
　
If the heater is good test the defrost thermostat. This should normally be done when the evaporator is still covered with ice since it will only activate at 40f - 50f depending on the thermostat. When tested with the ohms meter at below 40f it will read infinite. It is normally clipped to the upper right of the evaporator and look something like this:
The next possible problem could be the defrost timer. If you have tested the heater and thermostat and they have tested good next find the defrost timer, If your refrigerator has a mechanical one it will either be located inside the control panel in the fridge or behind the panel below the doors. Once you have located it advance the dial until you hear a click. This will initiate the defrost cycle. If your heater begins to get hot this will tell you that your timer has stalled and needs to be replaced. A typical mechanical timer looks like this:
If your refrigerator has a digital defrost timer you should locate the tech sheet. Normally you can find this behind the panel under the doors. It will tell you how to initiate a manual defrost cycle. As before if the heater gets hot you will have to replace the mother board normally located behind a panel at the rear of your refrigerator.
If your fridge is warm and there is no build up of frost/ice on the back panel inside the freezer then you problem is most likely going to be the evaporator fan, have you heard the fan running in the past few hours? if you are not sure pull the panel out to where you can see fan and watch it over the space of an hour to see if it turns. If you don’t see it turning replace the motor. This is what a typical evaporator fan looks like:
Hope this helps. If you have any other questions please feel free to comment again. If you decide to get a repair guy in should not cost you any more then $120 - $200 depending on make/model/problem Good luck & thanks for using Fixya! Mike

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.
OR
The evaporator coil behind the cover on the back wall inside the freezer will ice up under normal conditions. Every 8 to 10 hours for around 20 minutes the defrost timer (or in most newer models the electronic adaptive defrost control) will turn the defrost heater on to melt the built up ice. There is a defrost thermostat which prevents the heater from overheating the freezer by breaking the heater circuit when the temp reaches close to 32 degrees F. The entire cooling system shuts off during the defrost cycle and starts back when the timer advances through the cycle.

If this ice is not melted it will continue to build up until the air can’t flow over the coil to circulate the cold air through the freezer and into the fridge. The temperature change in the fridge is usually noticed first followed by the freezer.

If the defrost thermostat is bad it can prevent the heater from coming on OR it won’t turn the heater off when it gets too warm. It is clamped to the evaporator coil at the top to sense the temp. If it appears to be misshapen it is bad.
With an ohm meter it should show continuity when cold and none when warm.
You can also bypass the thermostat to see if the heater comes on then. If it does then you know the thermostat is bad and needs replaced.

The defrost heater is located on the evaporator. It is in a tube which is at the bottom and can also go up the sides of the evaporator. On some types you can see a burnt spot if it’s bad. With an ohm meter it should show continuity from end to end when disconnected from the wiring in the freezer. You can also test the wiring for voltage when it’s in the defrost mode.

If you have a defrost timer you can test it. It can be located under the fridge behind the kick panel on the front. Some are in the fridge with the controls at the top. You can turn the defrost timer till it clicks and everything shuts down. The heater should now come on. If it does, replace the timer because that means the timer is not running. If it doesn't, check the heater and defrost thermostat. Turn the timer again till everything starts back up to end the defrost cycle.

If you have an adaptive defrost control instead of a timer, replace it if the heater and thermostat test good. It is located in the fridge with the controls in some models and on the back in others.