DIAGNOSIS The thermostat control knob and its internal capillary tube sensor have likely failed. This is a common failure point.
FIX Unplug the fridge. The thermostat is usually located behind the interior temperature control knob. Remove the knob (it may just pull off). You'll see a mounting nut. Remove it to access the thermostat. Disconnect the wire leads. The entire thermostat assembly, including the capillary tube that snakes into the lining, must be replaced as one unit.
IF THAT DIDN'T WORK If the new thermostat doesn't fix it, the main control board is the next suspect. It may be sending a constant 'run' signal to the compressor regardless of the thermostat input.
HEADS UP When removing the old capillary tube, be extremely careful not to kink or puncture it. A puncture will release refrigerant and require a major repair.