[moltuae]

Back in the 90s, in my capacity as an electronics design engineer/programmer, I developed a fuel injection diagnostic device that also had an injector and idle control valve cleaner function. Idle problems due to clogged/dirty ICVs were a very common problem back then and most attempts to clean them in situ resulted in a fix that was temporary at best.

I'm guessing that a '97 A8 has the same early type of solenoid-based ICV. Later ICVs were controlled by stepper motors and were less prone to sticking. The solenoid type usually has 2 or 3 terminals. The 2-terminal variety are a simple spring loaded solenoid .... just apply power and it moves one way, remove power and it returns under spring tension. The 3-terminal variety use the additional terminal to reverse the direction instead.

What we found during development was that it was necessary to fully 'exercise' the solenoid, preferably while submerged in a cleaning solution. I think we used some sort of injector cleaning solution/detergent, but carburettor cleaner might work too. The most important thing is to pulse the solenoid from one extreme to the other while cleaning. In normal operation, the back and forth range of movement of the ICV tends to be much less because the ECU uses PWM (pulse-width modulation) to move it to the required position, so eventually scum-lines build up inside the mechanism either side of its usual operating range. Pulsing the solenoid back and forth to the extremes while cleaning helps to remove the scum-lines. The solenoids are not designed to be powered for long however, so its important to keep the pulses short (<1s) to avoid damage.

Edited to add: It's also important to observe the correct polarity when pulsing the ICV because they often contain back-EMF suppression diodes connecting internally across the terminals.

Having said all that, given that problem seems thermally related, it's also possible that the solenoid has an internal fault -- A broken winding wire can result in similar symptoms, making and breaking the circuit due to expansion/contraction as the solenoid temperature changes. However, it might be that the gunk is becoming more gunky when cold so I think it's probably worth trying a thorough pulsed-clean first.