Why Kenmore freezer gets cold but doesn't freeze.

Prepare to replace the t'stat. At least it is freezing and you haven't lost anything.

Is the compressor running?

usually when aq defrost timer goes bad it gets stuck in defrost. I would suggest replacing this first

Leave it plugged in. It won't over freeze. If the outside air is cold then it won't need to run as much to bring down the temp-nature is doing that. So when the weather gets warm it will run to keep everything frozen. Hope this helps. Google burdfrenzy

maybe the condenser is stock up or defective compressor or oil is in the freezers coil

Chest freezers don't normally self defrost. They just freeze. To defrost them, you must shut them off.

The light indicates the need for a new battery (9V)

a freezer is just a heat pump . from inside the freezer to the garage . the first law of thermodynamics says heat travels from a hotter to a colder surface . it could just be the cold how much are we talking?

check to see if your condenser is dirty, that can be the problem if looks clean, suspect low refrigerant charge