I first replaced the damper and thermistor thinking that they may have been the problem. But after a few days the symptoms returned. At that point the only thing that could be wrong was the control board, so I purchased one from AppliancePartsPros.com and followed the video to install it. The only issue I ran into was that I needed to press the refrigerator down arrow three times and not the freezer, so there may have been something strange with this part.
After I turned the power back on to the refrigerator, I needed to manually move the damper plastic cylinder a slight bit to the right for the board to realize it was stuck open, and everything worked correctly after that.