Michael; as John said pictures will be worth a lot as far as helping with diagnosis. It does sound like you're on the right track with the thermostat.

As far as the suction line getting cold; that may or may not happen. Most of these have capillary tube systems with a heat exchanger between the return line and the capillary tube. Basically, the cap tube is soldered to the side of the return line, along the length of it. This allows the warm liquid going through the capillary tube to heat the returning gas in the return line. Even on a properly charged system, often the return line is not cool at the compressor.

Freezers with R12 will often operate at very low suction pressures. There is not much mass flow of refrigerant going back to the compressor to cool it internally, so the compressor will be designed to radiate the heat out through the shell of the compressor. It may even have cooling fins on the outside of it to help it stay cool. After prolonged operation it may be quite warm to the touch.

Sincerely,

David