Kind of a shot in the dark, I'm not real familiar with Kenmore. Though I have seen a fair share of Amana and they are similar.
Most likely problem is frost build up. Either the timer stopped, the drain is plugged or the door was left slightly ajar. With serious frost build up, one defrost cycle may not be enough to clear the evaporator.
You can manually defrost by removing the plastic cover by the light, you'll see the timer behind a metal plate with a hole in the front. Insert a screwdriver and turn to the right until the compressor stops. After the defrost cycle is finished, let it run for half an hour, then repeat. Check the drain pan for water, there should be something in there, if not the drain line may be plugged.
There are so many models out there it is difficult to keep them all sorted out, if you have a model with the digital display, in your manual it will tell you how to manualy defrost in service mode.
There are other things that can cause similiar events, like the condesor coils being plugged with dog hair or dust. Refers are generally set up to freeze primarily and then cool the refrigerator part. When function starts to diminish, it may be noticed in the rfrigerator portion first.
There are often some other components associated with a defrost cycle. A thermal switch or thermistor to shut of the defrost cycle, when it reaches a warm enough temperature and some models have a seperate defrost thermostat built in.
If the timer isn't where I think it is, it may be behind the front kick panel.