Level of DifficultyA Bit Difficult
Time to do repair15 - 30 mins
Age of Appliance5 - 10 years
There is already a lot of good advice on this web site and others on how to diagnose and do this repair. I'll add a few additional comments that might be helpful.
I wanted to confirm that my old thermostat was in fact bad. I did this by disconnecting the two connectors and connecting them to each other to bypass the thermostat. This is like having the thermostat always closed. With the back panel still open so I could see the frozen coils I plugged the fridge back in and turned the defrost timer knob with a screwdriver to get to a defrost cycle. I could then see the heater element slowly melting the ice. This is of course not a safe way to operate the fridge. Over time this would get too hot and damage the food or worse. I only did this for a few minutes to see the system operating. I did not melt all the ice at that time. Also, it is of course dangerous to plug the fridge in with the panel open, so a great deal of caution is advised.
When I got my new thermostat I wanted to confirm that it worked before going through the install procedure. To do this I cooled it down and then used an ohm-meter to see that the circuit was closed. The important thing I found out is that ice-water, even 2 parts ice, one part cold water, was not cold enough to do this. Only when I put the thermostat into a cold freezer for a while did it get cold enough to close the circuit. I did this side by side with my old thermostat and saw that it was in face bad -it never closed the circuit.
This part from Part Select was an exact match for this freezer-on-bottom Whirlpool refrigerator. The connectors were identical so I did not have to solder wires together as others have need to do.
Some people get the ice off of the coils with a hair dryer. For me this could take half an hour. What worked better and much faster was spraying warm water on the ice with an old spray bottle. This adds extra water to the mix, but it did not overflow the drain pan. Even if it did, it would be easily mopped up if you can roll the fridge out.
One last thing. I suspect this thermostat broke in the winter, but with the dry air the fridge worked for a long time. Once summer hit and the house got humid, the coils iced up quickly.