Researched symptoms on web. Most common problem I found was a broken damper door. Per the advice I found here (http://fixitnow.com/wp/2006/04/14/ge-arctica-refrigerator-broken-air-damper-and-everythings-freezing-in-the-beer-compartment/) I disassembled things far enough to confirm that the damper door didn't seem to be working, so I took it completely apart and sure enough, the door had broken off the motor.
I'm about to replace the refrigerator as part of a kitchen remodel, and one of the sites I found in my wanderings suggested taping over about 3/4 of the opening as a temporary fix. I did that, with the intention of leaving it that way forever. It worked OK for a few days, keeping the freezer between 3 - 5 degrees, and the refrigerator compartment in the 34 - 37 degree range. But then something in the environment caused the fridge to drop down to freezing, and I said 'Screw it'.
So I ordered the part (WR49X10091) on a weekend, and it was on my front porch the following Tuesday. Sweet! Since I had already taken it apart once before, it went smoothly. It is now about 6 hours since I installed it, and everything is back to normal.
Suggestions:
I found it easier to remove the shelves and everything attached to the inside 'ceiling' of the refrigerator (light cover, light bulbs, light bulb socket mounting, water filter, and water filter shroud). Note, the shroud covering the water filter looks like it's screwed into the side wall. It isn't. Just pull the shroud straight toward the front of the refrigerator. As the link above says, you don't need to remove the rear tower assembly at the back.
All told, less than an hour. Even the first time, when I didn't know what I was doing.
Go for it!