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.