Yes, this could be a cause. The Bosch coolant temp sensor should have a resistance around 3000 ohm at 10 C and less than 700 ohms when the engine is up to operating temperature (around 80 C).

I switched from D jet to Megasquirt so it has been a while since I fiddles with Djet. I am not absolutely sure how D jet would interpret a broken (infinite resistance connection) on the CLT. If it just interprets it as really high resistance, it will be causing the D jet to interpret the engine as being always cold and inject extra warm-up enrichment fuel. This could explain the car running OK when cold and poorly when hot. However, when the engine is hot, the additional warm-up fuel addition would be causing the engine to run quite rich. I would think that this would be quite noticeable in the tell-tale odour from the exhaust pipe associated with partially burnt fuel mix. I think it would also show up in the colour of the spark plug insulators.

Checking the operation of the sensor itself is easy enough to do with an ohmmeter. If it is not shorted out internally or open circuit, it is probably OK (reads somewhere between 3000 and 700 ohms which will depend on the temperature). Check the condition of the wire close to the end of the plug which fits into the sensor. The wiring insulation gets brittle with age and exposure to heat and it may be shorting out or broken at the plug.

I think there needs to be clarification about if the car stops when it gets warm and does not restart, or if it runs, but dies off due to low idle speed.

If it does not restart easily.....I would concur with the diagnoses of the faulty coolant temp sensor, If it is a matter of idle speed not being hardy enough to run, then 142Guy's remedy applies.
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Antique Swedish Steel 71 142E color V#102

I finally found what I think is the idle set screw. It is on the underside between the manifold intake opening and the throttle body with a securing nut surrounding a screw. There is also an unidentified open brass nipple with nothing attached? Any idea what is supposed to be attached here? In reference to your instructions, I'll attempt to raise the cold idle tomorrow.