An air carrier jet declared an emergency and diverted to a nearby airport when they were unable to resolve a 'melting plastic' odor.

Narrative

A Flight Attendant called and reported a 'strange odor' in the aft galley area. Another flight attendant said it smells like melting plastic and advised the passengers were complaining about the smell. No one was in the Lavatory and the odor was definitely coming from the galley.The First Officer and I ran an appropriate check list turning off power to the galley and entertainment systems. I called back to see if the procedure helped. She said the odor was still there and possibly getting worse. I made a radio call to Center; declared an emergency; advised we needed to go to ZZZ and requested CFR be standing by. Descent and landing were normal. CFR checked the aircraft for heat. No exterior heat was found and they asked if I wanted them to board the aircraft. I said yes and informed the Flight Attendants to disarm the left aft door. They located the heat source in #4 coffee maker. Company Maintenance; who had come on board with them; removed the coffee maker and found the internal circuit breaker blown and a fried circuit board. With the all clear I proceeded to the gate had the coffee maker replaced and we continued to our destination. The Flight Attendants did an outstanding job of keeping me informed of the situation and calming the passengers.