here's my scenario:
1990 vw fox california car - with an ICU [tried that didn't fix] not sure on the digifant - but anyhow - car runs when first starting up, cuts out when warm ... the type of die is a like cut no spark thing and even back pressure and puffs out this grey smoke from the air filter area - like back pressures out. i can then get it started again
- will run great cold for a while and play with throttle a bit works
- full or partial throttle when warm does this death / cut out / diesel / chokeded out thing
- tried the timiming light and it gets spark as it dies
- tried the accumulator - though that didn't make a difference
- when warm i can get it running again - just seems like a more often when warm and like totally random
- definitly not driveable as cuts out and will kill battery trying to start it

that one looked to be disconnected - i reconnected the vacuum line and it made no difference and i can feel vacuum from the line that attaches it - i am thinking maybe the ECU?! please help - or maybe as boschman suggests a fuel vw specialist with proper tools - dunno please advise

Did you say you have Digifant? I know non-Cali '90 Foxes would have CIS-E. Since you said you replaced the ICM I take it you have Digi II, as Digi I has it built into the ECM. I would still suspect an ignition problem because of the backfiring. I had a similar problem with a Digi I vehicle (would run fine for about one minute then would falter, hesitate, spark knock, & backfire when the throttle was opened). But in that case it was actually a problem with the Hall sender unit in the distributor. I can give you ways to check that if you need, but mine checked fine & was still the problem. It had to do with the advance mechanism in the distributor I think. You can clean & lubricate the connector at the distributor too. If you have either Digi you can easily check fuel pressure with a simple gauge at the test port on the fuel rail (about 40 psi running). Also checking the temp sensor is in order since it seems to be temp related. I just posted on checking this on the "fuel in oil" thread in this forum. I'd still go with an electronic ignition problem though, I assume you've checked cap/rotor/wires/plugs.

insteresting - when i advance the timing - the problem goes away
or is not as pervasive - i am thinking now the distributor as boschman pointed out - i suspect it would pass the tests also - i checked the advance spring and seemed to work fine - sprung back - dude it seems to me as you posted this reply i was outside screwing around with just that - and drove it - WITHOUT dieing - of course pinging a bit - too advanced... - so maybe i'll go and pick up a distributor - shouldn't be too much - thanks boschman for the vdub help

Don't forget about that electrical plug connector to the distributor. I've had alot of trouble out of them too.

I had this same exact problem for months - couldn't figure it out for the life of me - turned out that the fuse for the electronic fuel injection on the bottom of the fusebox was blown - replaced it and the prob was solved - hope this helps! :)