We have an old (c 1980) GE 'Frost Free' fridge
(freezer-on-top).

CY: Ah... generally expensive brand.

Both
the freezer and the fresh-food areas cool down only to about
50F. The
evaporator fan runs, and seems OK. The evaporator coils are
'cool', but
not so cold it hurts to touch them. The defrost heater is
not on.

CY: 50F is a bit too warm.

The compressor runs, but shuts off after less than 10 mins.
The
compressor is quite hot - you can touch it, but it would
burn, if you
applied pressure. (The compressor fan is running, but shuts
off along
with the compressor.)

Questions:
- Is that too hot for a compressor? IIRC, my father used to
say that a
motor that you couldn't touch was too hot. Even if true,
does the same
apply to compressors?

CY: I think your Dad is right. Sounds like the compressor is
running way too hot.

- Would they have a 'self-resetting' temperature cutout on
the
compressor, where it would keep recyling after cooling down?

CY: Yes, there is such a device.

- Any other reasons why the compressor would shut off, when
the freezer
is nowhere near the setpoint temp?

CY: Either too hot, or too much current draw.

Thanks,
George

CY: As you didnt ask for ideas what is the problem (or how
to solve the problem and make the fridge work again) I'll
limit myself to answering your questions.