Similar problem
I just picked up a sweet 87 325es on a trade yesterday, and I'm trying to get it running smoothly. I found this thread in google so I figured I'd run it by you guys. I'm hoping it's NOT the ECU/DME as an ICV or TPS would be a whole lot cheaper.
Basically, to start it, I have to give it gas for it to 'catch' and let it warm up with my foot on the accelerator to have a chance for it to move after i put it in gear (Automatic). During this time the exhaust smokes pretty bad, but after it gets going the visual smoke will clear (but the smell still remains). If I am stopped at a light it will die unless i keep a foot on the gas the whole time.
However - I've noticed that if I take it on the highway, after I exit the problem goes away and it runs like it should, very occasionally hesitating from a stop after I give it some gas. When I park it after letting it run at highway speeds for a while, it will not die but the idle speed seems to go up and down (the tachometer isn't working - but that's a seperate issue. Someone told me that it needed a battery? Maybe they're blowing smoke up my ass.)
The guy I got it from showed me something in the glove compartment and he said that's what would get it fixed... He didn't know what it was called though.
Am I going to get away without replacing the DME? Any and all help would be appreciated.
EDIT: So I got in the car which had been sitting in the 90 degree weather - started up just fine. Idle speed fluctuates though.