2004 Volkswagen Passat Turbo post-driving idle time

The issue isn't cooling down, .. Exactly. It's running the turbo without oil pressure. Oil pressure drops to 0 pounds as soon as the engine stops but the turbo can keep on spinning for quite a while, especially if you were just driving at higher engine speeds. The rule of thumb used to be to let the engine idle for one minute to give the turbo time to slow down but that is rarely followed. If you pull into a parking lot you'll be driving slow enough that the turbo will already be slowed down by the time you stop the engine. Probably the most harmful thing you could do would be to shift to neutral at highway speed and stop the engine to coast down a long hill and save fuel. You can still save fuel by letting the engine idle while you're coasting. I'm not recommending you do that. I caused damage to a transmission once when I accidentally shifted it all the way to reverse at 55 mph. The damage didn't cause a total failure for a number of years, but when it did fail, I knew the cause.

The owner's manual will have the final say in the correct procedure. If nothing is stated you should be fine if the engine is running at idle or a slow speed for 15 - 30 seconds before stopping the engine.

Don't be too hard on him. He's probably remembering the warnings from many years ago. Chrysler started using turbos a lot in the '80s and they had good luck with them. Ford copied it later but they had a real bad problem with "turbo lag". That means it takes a couple of seconds to respond after you press the accelerator pedal. It was very annoying but it was "the nature of the beast". The turbo did not spin at idle, or it ran very slowly. Their concern was if you pulled off the highway and stopped the engine right away, the turbo could still be coasting to a stop but the oil supply to the bearings would stop. That can have catastrophic results. They recommended letting the engine idle for one minute to insure the turbo had stopped spinning before the oil flow had stopped.

In the second of Chrysler's three generations of turbos they averted that turbo lag problem by keeping it spinning when the engine was at idle. That kept it ready to produce power in an instant, and that innovation made big news in the industry. Because it was spinning all the time they knew it would always be running at idle and when the engine was stopped. To address that they used improved metal alloys and modified the oiling system. Turbos can easily exceed 100,000 rpm so that oil is critical but now it became more of a cooling issue. The oil carries heat away from the bearings. That is not a concern when stopping the engine.

To add another dimension to the story, my friend owns a body shop where he specializes in rebuilding one and two-year-old Chrysler products, ... Mainly Dodge trucks. He kept three with horrendously powerful diesel engines and those all use turbochargers. There has never been a discussion about how to stop those engines. Those turbos are a lot larger and beefier than what's used on cars, and they're real expensive, but failures are almost unheard of. If there was a serious and legitimate concern about engine stopping procedures, those truck guys would be talking about it.