From the blog "Samurai Appliance Repair Man's Blog"
One of the many things that can make a refrigerator warm up is the compressor is trying but failing to start. You may occasionally hear this type of noise from the back of the refrigerator (starts about 15 seconds in):
This is the sound of your compressor trying, but failing miserably, to start. Best case scenario: Bad compressor start relay. Worst case scenario: open compressor start winding or seized compressor bearing == buy a new refrigerator. Question: How do you tell which is which? Answ