Autobox thump / Sticky cold start

Pity we are not paying 1980's petrol prices! the sad thing is my mate is
getting better mpg out of his v8 M5 and he drives it like a rental.

I've just done another tank of the most economical driving I can muster and
averaged 19mpg based on miles/gallons.

With regard to the thump problem, checking the service history reveals,
engine mounts, gearbox mounts, Bushes, Gearbox oil and Diff oil were all
changed at the last service (2000 miles ago). Maybe this was in a bid to cure
the problem which failed.

Dispite the cold start issue happening nearly every morning now I still love
the car

Update on issues:

I have replaced the DME with the 0 261 200 179 model which technically should go in an '89 car and this has cured the cold start problem and in many respects made the car better. However tickover is now a bit lumpy and fuel econonmy is only slightly better.

With more time to monitor the gearbox thump I have realised that it is much worse when the car is cold which I think suggests either a worn box or bad oil. I need to replace the oil cooling pipes anyway so I will do a complete oil change at that time and see if it improves.

The strange bit is that the new DME immediately improved the thump so now it only really occurs under hard acceleration or randomly.

The other thing I've noticed is that the box now has more tendency to hunt between gears at slower speeds, e.g. 40mph. Suddenly the car will feel like its dying but in reality it has kicked down a gear and the engine is braking the car.

Whilst my car requires the 1 261 200 150 DME I'm told that any DME from an 3.5L M30 engine around the same age will suffice (e.g. e34 535i and e32 735i) and in my experience it certainly works but I wonder if there are some small incompatibilities?

Are you measuring MPG via the OBC? My 735, after a repair, was returning 19 ref the OBC. Turned out it had been reset as US gallons. When set to Imperial, MPG improved to 24.5!

Might be worth resetting by the small indent lower left on the OBC.

Edited by eta.

-do change the oil filter in the gearbox when you change the oil- this will likely be clarted up.

Also (and this might seem bloomin' obvious but then again not) do make sure that you check the oil level in the gearbox when the engine and tranny are fully warm, and the engine is running, as per the owner's manual.

cheers