Reasons that a GE refrigerator doesn't cool properly include ice buildup on the back wall or the door gaskets not sealing properly. Cooling problems may also be caused by dirty condenser coils or not having enough air clearance under the unit.
If the unit is newly installed, it may take up to 24 hours or more for the refrigerator to cool down and properly stabilize the internal temperatures. If the refrigerator was just serviced and suddenly won't cool down, it could be a sign that it is still in diagnostic mode. To see if this is the case, unplug the unit for 30 seconds, and then plug it back in to see if it starts cooling properly.
In order for the refrigerator to cool properly, air needs to circulate throughout the inside of the unit. Large objects or ice at the back of the refrigerator can interfere with the air circulation, causing the unit to fail to cool as effectively as it should. In addition, not having enough items inside the refrigerator can also negatively affect its cooling potential. This is because the more cold items are present inside the refrigerator, the less cold air the unit needs to produce to cool itself back down after the door has been opened.