That sounds as though the engine thermostat has stuck open?
It would explain why the temperature falls once you start moving - but I would have thought that it would have to be very cold outside for this to have a noticable effect?

It would also explain the rough running, if the engine management system thinks the engine is cold, it will run the engine on a richer mixture (as if the engine was just started).

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'02 X5 3.0d, Auto, Topaz Blue