If the fuel shut-off solenoid fuse was bad it would not start at all. What is being suggested is to check if the temperature switch part # is RE503242 is plugged in, this is part of the cold start advance. I have attached a write up on how the cold start advance works.
To comply with the exhaust emissions regulation, the timing of injection pump should be around 6 to 9 degrees before TDC. These timing values do not allow proper start-up operations when engine is cold. To ease engine start-up, a cold advance system gives to the injection pump a temporary over-timing.
When coolant temperature is below 50 C (122 F), the solenoid valve is activated and opens the cold advance circuit.