Could be the wiring or connector to that #3 coil. The wires inside the harness that runs along the top of the valve cover sometimes get cooked/brittle with age and the insulation will break up and cause shorts.

It could also be the ECM. Each coil has it's own trigger signal output from the ECM. If that output is dieing, you'll lose spark trigger pulse and the coil won't fire. Sometimes semiconductors fail in such a way that they work normally till they heat up.

Double check the ignition system grounding point on top of the valve cover between cylinders 1 and 2. It looks like one or two brown wires fastened under a valve cover nut.

 

Grounding is fine.

Hmm. Since it happens only when hot, your suggestions lead me to believe it needs a new ECM. I can get a used ECM locally for $30. But, if my research is correct, we can no longer get PIN numbers from the dealers for the immobilizer, right? So with a used ECM, I need to take the whole damn car to the dealer to get the used ECM adapted, right? Or is there a way I can do it with VagCom?

Keen

 

Update: It was the ECM. It runs great now.

And may I just say; P*ss on my local VW dealer!

I drove the car to the dealer, and handed them the new(used) ECM. I had taken off the plastic shield over the ECM, taken off the wipers and plastic wiper guard, and left the screws out of the ECM container. All they had to do do was hook it up to the scanner that calls Germany and downloads the codes, swap the ECM (3 minutes if you're an idiot), and wait for the programming to finish. They charged me for 1.5 hours! Flipping $166 for 10 minutes of ACTUAL work! All because their little book says it takes 1.5 hours to do it. Bast*rds.

All this after the service manager insisted that I had diagnosed it wrong, because ECM's never fail. Moron. And the dealers wonder why anyone who knows a little about cars hates them! This is the first (and last) time I've used service at the dealer fo 30 years!

Rant over,
Keen

 

Yup, the common lament is that the cars are much better than the dealers. I assume you first checked whether you could do the code transfer with Ross Tech's VCDS/VAG-COM.

 

I take it that it had too many miles to still be within the part of the emissions warranty that covers the ECU?

 

I assume the emmisions warranty is expired. It has 134K on it, and is 10 years old.