On my old fridge AND my new one (-new one because it's the right color - the old one is now at my office, and still running stron after at least 15 years) the defrost timer is on the back - exterior of the refrigerator.
It's there because everytime you open the door, moisture laden air enters the freezer, and that moisture condenses and freezes on the coils, which are behind that pretty white plastic lining inside the freezer compartment.
The timer basically turns off the compressor (or perhaps makes it run in reverse for a minute, blowing HOT gas through the coils melting the ice) for a period of time long enough to free the coil of ice. The liquid then runs down a tube and is deposited into a pan under the fridge where it evaporates (sometimes with the aid of a small electric coil heater to hasten evaporation).
Anyway, I just manually cycled the timer, and checked it with a meter. It didn't do what I thought it should, so I put on a new one, and it fixed it.
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One way to check it is to empty the fridge, unplug it for several hours, and plug it back in. If it begins to work properly, and then slowly loses it's ability to cool, this is probably your problem.
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The defrost timer is almost the only thing on a fridge associated with the cooling system that ever breaks. People usually replace them for reasons of style, or the plastic bits in the interior of the device break - shelves, etc...
Good luck.
[of course, your mileage may vary...}