PJ, it's fairly easy to check the thermostat. First, remove the cover from the front of the ice mold mechanism (white plastic, 4" square, on the very front of the icemaker unit inside the machine). There are two slots at the bottom of it. Insert a screwdriver in one of the slots and twist it. Note: you'll usually crack it when trying to get it off, no big deal. It usually just cracks in the corner, making it easier to remove next time.
When you've got the cover off, locate the SMALL gear. The newer ones are metal and have a hex molded on them, to allow you to put a small wrench on them. (the older ones were plastic, and had no hex on them) But if it is, say, a 1985 or newer unit, it will have the hex on it.
With the machine on and running, grab the hex with a wrench and force-turn it about 1/4 turn COUNTER CLOCKWISE. Remove the wrench. The compressor and fan should immediately shut off, and the gear should continue to turn. Within about 5-7 minutes' time, it should continue around, dump any ice that is in the mold, bring in new water for the next batch of cubes, then park itself and the compressor and fan will come back on and begin the cooldown cycle for the next batch of ice. If it does all of that, the thermostat is bad and needs to be replaced.
The thermostat is located on the right-hand side, behind the lower grille. You'll see a round decal with an arrow, saying "Colder." That's the thermostat (U-Line calls it the cold control). There are (2) screws holding it in place. Before trying to remove it, turn off the power to the unit, at the breaker panel (don't just shut off the switch on the front of the machine). On the rear of the thermostat are several wires. Be sure to note which wire connects to which terminal on the thermostat. The tabs are numbered on the thermostat - don't just go by the position of the tabs, mark down the actual number (red goes to #3, etc.). The replacement thermostat may not be laid out exactly the same as the original, so the position of the tabs can't necessarily be trusted.
Next, the machine will have to be removed from any cabinetry where it might be mounted, as you need to get to the back side of it. A long capillary tube goes out the back of the thermostat, through the lower portion of the machine, up the rear of it, and it goes into the rear of the ice mold unit.
Pull the capillary tube from the rear of the ice mold unit, and fish it out through the front of the machine. Remove the old thermostat unit completely.
On the new thermostat, straighten about 12" of the capillary tube, and feed it into the tube in the rear of the machine where you removed the old one. Push it in until it "bottoms" inside the tube that protrudes out from the ice mold unit. When it has bottomed, bend the capillary tube sharply and feed it down the rear of the machine and gradually unwind the rest of the coiled capillary tube and fish it through the machine from the rear to the front.
Re-connect the wires, then turn the screw adjustment all the way counter-clockwise (to the warmest possible setting). Leave it at that setting. Then let it hang by the wires and turn the machine back on. If, after 2 hours, everything seems to be working correctly, turn the machine off, mount the thermostat in its permanent location and replace the lower grille. You're done.
If it doesn't work properly, double-check the wire connections on the new thermostat, to be sure they are correct. Again, only go by the numbers on the individual terminals, they may not be in the same respective locations as they were on the original.
Note: always leave the thermostat in the warmest possible setting, unless the ice is wet and soft.