Bought the car in the fall and experienced this problem first just the other day when outside temps got over 70. Car ran fine on the freeway at 70 mph, but stalled as I was slowing for the red light at the bottom of the off ramp. Started again with my foot on the throttle, but didn't want to idle right. It would die, or the idle would drop to almost nothing, then jump up to 1500 rpms and repeat. I was not far from home so I drove two-footed until I was home and shut it off, in no mood to deal with it.
About an hour later I went to start it, thinking perhaps it was an engine temp related issue. It wouldn't start, and there were some strange noises coming from the back of the car. The fuel pump would make it's usual buzzing noises after cranking and no start, but then I would hear a rumbling noise that I wasn't even sure was coming from the car. After a couple more tries to start with the same strange noise, along with an odd groaning noise that I can only describe that way. I opened the trunk and heard that the rumbling was actually a gurgling noise coming from the tank. I had to be somewhere, so I jumped in the beater VW and left.
About three hours later it was about 10:30pm and much cooler outside so I tried again to start my 400 and she fired right up like there was never a problem. At this point I was suspecting some kind of fuel issue, but wasn't sure what would cause these strange noises, or how outdoor temp was affecting it.
Weather cooled a bit for the next couple days and I had no problem.
Today it is about 80, I drove the car all morning running errands with no problems, and parked the car in the drive when I came home. About an hour later I went out to start it and it just cranked over, no cylinders firing, and again with the gurgling noise. I suppose I could wear out my starter, and use some throttle to get 'er going, but I would really like to figure out the problem.
I did a search in Tech Help and found a couple other 400/420 owners who have had the same problem, complete with gurgling noises, but no resolution showed up in their threads.
Has anyone figured this out yet? I would prefer not to start throwing expensive parts (fuel pump $250-$300) at this trying to figure this out.

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Fourings

84 Audi Coupe GT with Turbo engine, EFI (buh-bye CIS), Jamex seats, Koni's/H&R's, e-code lights. 210k and counting.
1992 Anthracite 400E, 161k, "Grey Ghost".
1986 VW Quantum Syncro, 192k, gone to the crusher in the sky.
1989 300TE 172k. (Was mine, now also Mom's car)
72 280SE 4.5 (Mom's car)