325i noise from engine/trans at idle cold
 

My 1991 325i has 179000 kilometres on it and it has the ZF automatic transmission. The car is in excellent condition and has never been damaged. When I bought the car at 172000 kilometres 18 months ago I had the transmission served by a transmission shop and they said it seemed OK. I only had it serviced as a precaution or because I thought it was a good idea.

My current problem is a noise at idle when the car is cold. It sounds like a wobbly pulley. It is NOT there for the first 20 or 30 seconds and disappears after a few minutes. It seems to be worse when reverse is selected and I reverse out of the driveway at idle.

I described the noise to a BMW workshop and they replaced the belts and the belt idler bearings. The noise was still there when cold and I took the car back to them. They had the car overnight and when I picked it up they were unsure what the noise is. I wondered if it was a loose baffle in the exhaust but the BMW workshop said it sounded like it was coming from the vicinity of the transmission.

I took the car to the same transmission workshop who serviced it previously but it was not cold at the time. He could only make suggestions and thought perhaps the spring plate may be slightly loose or the high pressure in the pump when reversing on a cold motor may be cause.

The only other slight problem with the trans is it seems to bang slightly back into low gear when slowing down almost to a stop.

Can anyone help with this please.

Thanks

Perhaps I should make it clear the car is an E 36, an early one.

Thanks