I'd first bleed the system to ensure there's no air pocket and ensure waterpump flowing properly. With the engine off and cool, remove the plastic bleed screw and fill the expansion tank untill coolant comes out of both holes. Then re-instal the bleeder screw and start the engine. There should be a stream of coolant flowing across the opening where the fill cap goes. If no stream there, have someone hit the gas to about 1500-2000 rpms and look for it. The stream should be pretty strong then. If no problems were found/corrected with that, then may be time to take it in for electrical diagnosis at the dealer as the temp readings and fuel mileage are determined by the DME and signale sent to the cluster via can bus. Not many simple circuits on the beemers, but the coolant temp sensor is a regular NTC sensor.

Even in the morning when the car is cold I can turn the ignition on and the temp gauge goods off the scale past red. So its not engine related.
Its more instrument cluster related, due to both MPG gauge and temp gauge acting up at the same time.

When you first turn on the key the cluster does a self check... all the needles do a full sweep then return to the normal positions. If that is all it is doing, then thats normal.

Does this happen only when you first turn on the key, or while driving?

mine never does a self check, and neither does my friends. The only time a self check happens is when power has been removed.
The temp gauge stays in the red for 5 mins, then drops to blue and steadily climbs to centre when warm.

what yr X5? engine? how low a temperature is your coolant good for? if you have alot of miles, has the water pump been also replaced (given you've replaced the t-stat)? - these are the 1st questions I would ask myself - everything else noted here already is good & maybe needs to be addressed also, but it helps to know the whole picture before giving advise