I don't know about the E30 auto but we ran into this several times with E32's and E34's. The details were this: If started from cold and idled, you can safely idle at up to 2500rpm (not higher) without engaging the internal clutches. If you idle higher than that at any given point, the clutches are engaged in some fashion, and will proceed burn themselves out if the engine is maintained over idle speed while stationary after that, even after a period of normal idle. In order to return to a safe elevated idle condition, the car must be shut off for a minumum of 1 minute. Then idle speeds up to 2500rpm may again safely be attempted.
Around here, the idle test is run *at* 2500rpm as part of the E-test. Tricky business for your transmission! Hope the test guy is a) good and b) understanding of the issue.
We had a lot of burnt out clutch packs in these autos when the E-test first started up.
-Russ.