the idle speed is controlled by an ELR unit, its a relay type box behind the battery curtain.

Its fed by the overvoltage protection relay and its job is to make sure the engine remains at 640 rpm at idle whether in gear, A/C running, power steering loaded etc..

Without its assistance the engine should be at about 550 rpm - measure with a tach tool or a MM that can measure Hz. - the rpm sensor reads 144 teeth every rotation of the flywheel.

Make sure the wiring is good and intact - as shorts in the 4 wire coolant sensor circuit can cause the idle speed, EGR and also the manifold flaps to act completely bonkers.

You mention the car idles at 700 rpm, this makes it sound like the alternator is not working - there is no load on the engine at all.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)