1st to check is thermostat, if mechanical type, (rotary Dial) can you hear it click on/off, If no click faulty thermostat, replace, easy, if clicking, when on, lower position, does compressor motor start. If not, any other device in use to stop it, auto defrost etc.
If need more help, Post with Make model etc, the more details, the better the answer
SD
December 2011