Fresh food temperature looks OK but the freezer temperature still seems a little high but this is probably due to the thermostat setting you are using.
Should be 0 to 5 degrees F.

Yes there is a thermostat, Item 3 in Section 2 of the parts.
But it controls just the freezer temperature.
The problem here is that the unit is trying to reach a set point but cannot for some reason so the unit runs all the time.
So I doubt this is your problem.

Now that the condenser coils are clean, check that the condenser fan is running.

If it is remove the cover from inside the freezer and inspect the evaporator coils. If the frost is only in one area or blotchy then you are probably low on freon.
This will be an expensive repair as you will need a pro.
Often it makes more sense to put those dollars towards a new unit.

Here is a good link
http://www.applianceaid.com/refrigerator.html
Cneck out #20 and then the 3 example pictures part way down the page.

Click on the picture of the part for more views of it.
You can then click on those pictures to expand that picture.

[COLOR="DarkRed"]Is there a "thermometer" or temperature measuring lead (thermistor?) that goes into the thermostat?[/COLOR]
There is no thermistor the temperature sensing is part of the thermostat, see below.

Read more: http://forum.appliancepartspros...ing-2.html#ixzz1OxwTJLhx
http://forum.appliancepartspros.com


The freezer thermostat (Item 3 in Section 2). Is an analogue thermostat so the curled end is the temperature sensing device and it feeds back through the metal tubing to open/close the thermostat's contacts.

The fresh food thermostat is part of the damper (Housing ass, auto) (Item 8 in Section 3). Basically it is the same as the freezer thermostat but instead of controlling a set of contacts it opens/closes the damper door. There by regulating the amount of cold air that enters the fresh food section.

[COLOR="DarkRed"]The unit runs all day, but turns off for ~20 minutes for the defrost cycle (seems like every 8-10 hours). Condenser fan by the drip pan and condenser coils is running. Evaporator fan runs. The frost coat on the evaporator coils covers the entire assembly evenly.[/COLOR]
Everything above seems normal so I am at a loss why the compressor is constantly running. If the main thermostat was sticking closed then the freezer temperature should be much colder but if anything it is high.
Are the kick plate vents clean?
Is the ambient temperature high?
The condenser coils look like the jelly roll type are you sure they are clean?
Usually you have to blow these out with a compressor as a cleaning brush will not get in there.
Something is causing the unit to not run efficiently but for the life of me I cannot think what that could be.