My GE refrigerator quit getting cold. I tried cleaning the coils and cleaned under the frig. I replugged it and set the temperature accordingly. The temperature went back to 70 degrees.

You have a problem with the defroster. When it is not running properly the fridge will not get cold due to all the built up frost on the coils inside the condenser portion.

Also can you hear the evaporator fan running when you open up the fridge and freezer portion? If you don't hear the fan then the fan motor went and you need a new one.

You want to check both fans: the evaporator fan in freezer and the condenser fan under refrigerator. Also, check your defrost timer. It is a box with a lot of wires going to it and a one-way plastic screw slot on the front. It can be under the refrigerator or inside next to t-stat. Look around and you will find it. Many times they are on the front bottom of the refrigerator behind the kick plate. Turn it and when it clicks everything will turn off and the defrost heater inside freezer should come on. Wait and see. After a while you should be able to hear it and see steam rising. If nothing happens and refrigerator comes back on you most likely have a problem with the defrost heater. If refrigerator does not come back on in 15-20 minutes then your defrost timer is bad and you need to unplug the timer and get one that matches. Unplug refrigerator first. Otherwise, follow these instructions: If it is a normal type it has a defrost timer which turns off the fan in freezer and the compressor and energizes the defrost heater until the terminator t-stat turns it off or the timer turns it off, whichever one is first. It's a very straightforward system that is easy to work on. The electronic ones are totally different, but normally when they go bad only the heater and terminator needs to be replaced. Just remove the cover to coils in freezer to access heater and terminator. Don't forget to clean the coils under unit, too. Many times the timer is under the unit near the coils or near the t-stat in the refrigerator section. Let unit thoroughly defrost before working on it. After removing the cover to coils you will see wires leading to a heater attached to the coils. On a side-by-side the heater is a glass rod with an element inside that you can see if it is bad; on a freezer on top model it is aluminum and wrapped around the coil that will burn apart often. There is a defrost t-stat attached by wire to one side of the heater and clipped onto the coils. It is round and has two wires, one to the heater and one to the power from defrost timer. With refrigerator unplugged turn timer until you hear it click and stop. Have wires unplugged to defrost heater and defrost t-stat and get the plug and the wire supplying power to heater. Put meter on ohms and put one lead on wire supplying power to heater and one to plug prong and if timer is good you will read about zero on both prongs – one to each wire supplying heater power. Then put one lead on each side of heater and if you have no continuity you need a new heater. Replace heater and terminator together and be very careful when replacing it, especially on the freezer on top model because if you bend the wrong thing you will break one of the delicate capillary tubes and lose all of the Freon which will ruin the unit. DrTom4444

Sometimes you have to let it stay unplugged for a couple hours to reset itself. Cleaning coils should be delicate and use less water as possible. Check freon