Refrigerator problem

I have a Magic Chef 3.6 cu. ft. Model#mcbr3605 thats 3 years old and has stopped working. When I plug it in you hear it start then you hear a "click" and it turns off. If you leave it plugged in the compressor gets hot. Can this be fixed or is it trash ? Thanks in advance.

Our Magic Chef compact refrigerator (model # MCBR445W1) completely shut down after one year of use. We used a multimeter to check the continuity of the C and L terminals located on the defrost/temperature control unit in both open and closed switch positions. The test verified that there was a short in the defrost/temperature control unit which had to be replaced. The temperature control unit is located behind the defrost/temperature control dial inside the refrigerator. Since the unit was purchased at Home Depot, we called them to order the replacement part. Our local Home Depot store advised us to call 877-650-2121 to order the replacement part. The part cost was $28.20 + $6.00 S&H. As we had taken pictures of the defective part as originally installed and noted the wire connections by color code and terminal position, it was easy to install the replacement part. The fridge is now back in operation at proper cooling levels.