That solenoid is used to control idle speed, and yes the EDS computer looks at coolant temp to see what the idle speed should be.

If the motor is missing when cold I would look at the glow plugs, injectors, and injector timing.

-J

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1991 350SDL. 230,000 miles (new motor @ 150,000). Blown head gasket

Tesla Model 3. 205,000 miles. Been to 48 states!
Past: A fleet of VW TDIs.... including a V10,a Dieselgate Passat, and 2 ECOdiesels.
2014 Cadillac ELR
2013 Fiat 500E.