The cold start valve sprays fuel only when the engine is "cold" to the temperature switch, and only during cranking. You have to pull it and check it during cranking with a cold engine -- I don't know the temp, but would guess 50C or thereabouts, not higher. The usual problem is failure to open at all, or leaking during operation. It should not drip at all with a warm engine, or at any time the starter isn't operating. All computer controlled these days, so I can't help much -- most of my experience with K-Jetronic is from twenty years ago on my 1975 Audi Fox. All mechanical in those days. May still be, but I don't know for sure.
The mixure is controlled by a "frequency valve" that regulates the return pressure -- called the electrohydraulic pressure regulator.
I'm glad a new fuel distributor helped, but that is a very expensive "hope it works" kinda thing!
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!