Got a 300CE-24 with KE Jetronic. Had exactly those symptoms.

Checked resistance and various temperatures of all the temperature sensors. The air intake sensor was open circuit.

Changed it (€12 at MB) and that altered the duty cycle from around 50% to 90+%. Adjusted it back and the only problem then was a minor hesitation after hot start. New Beru (€20) spark plugs cured that.

All this is with the original 19 year old 300K KMs distributor cap. I'll change that next.

Look at the cheap things first.

RayH

PS: mespe said, "I don't see the correlation between the engine being hot (up to temp) and the car running bad after a restart, and the fuel pressure, when the car ran fine before it was shut off."

I do!

When the engine's been off for a few minutes air intake temperature rises considerably. The entire engine compartment is hotter and the fine tuning really needs to know about the heat in the air intake.