The lower half of the filter box is attached by a single bolt and two pipes. Undo the bolt and use a long, flat-bladed screwdriver to loosen the Jubilee-clips:

Disconnect the plug from the MAF (Mass Air-Flow meter), loosen the large Jubilee-clip and remove.

Expansion  bottle and fan shroud removal

 With the MAF and airbox removed access to the expansion tank can be made disconnect the coolant hose:

Remove the expansion bottle cap, remove the vent plug and then prise this piece of plastic from around the bottle:

If this is the first time the expansion bottle has been removed, the return pipe will be fastened with a one-time use clip. The clip has to be cut off using end-cutters. On my car there is a Jubilee clip, disconnect the top pipe from the expansion bottle:

Disconnect the plug from the coolant-level switch:

The cowling is held in place by two expanding rivets, pull the centre out and remove both rivets:

Remove the weather strip:

Lift the cowling, pull the expansion bottle up and out, if you are doing further work on the cooling system, disconnect the plug from the AUC controller. Otherwise, it's out!

Refitting the expansion tank

Slot the lower part of the expansion bottle into the cowl, lower the cowl further and re-connect the coolant-level sensor:

I found the next bit awkward, it might have been easier to disconnect the small-bore coolant pipe at the radiator, but this is how I did it: Lower the cowling almost fully down and push the small pipe through the aperture in the cowl towards the expansion bottle. Push the pipe fully on to the bottle and tighten the Jubilee-clip through the vent hole:

Push the cowl fully down, push the expansion bottle in place and refit the plastic catch:

Lubricate the vent-screw seal with silicone grease:

Fit the lower pipe:

Refit the expanding rivets and the weather strip:

Refitting MAF and airbox

Lubricate the inside of the large-bore air pipes with silicone grease, this makes it easier to get the airbox in place:

Refit the MAF and reconnect the plug, use silicone grease on the large o-ring seal. Refit the lower part of the air-box, ensure the rubber mount mates with the aperture in the bodywork, tighten the Jubilee clips and replace the mounting bolt:

Replace the filter element and clip the air-box lid in place, refit the air pipe at the front.:

Filling and bleeding coolant

Use a 50/50 mix of BMW coolant and ionised (or distilled) water to refill the system. You should only lose a gallon of coolant at the very most. But it is always best to follow the complete bleeding procedure:

1. Re-connect the battery

2. Switch the ignition to position II, do NOT start the engine

3. Set the heater to 32C on both sides, fan at lowest speed (but not OFF)

4. Loosen the bleed-screw two turns

5. Pour the coolant into the expansion tank, if the coolant reaches the neck of the bottle fit the cap and tighten the bleed-screw, squeeze the top hose a few times, remove the cap and loosen the bleed-screw

6. Once you have at least 6 litres in the system, start the engine and position the car facing up an incline (or drive on to a pair of ramps)

7. Stop the engine, then return the ignition to position II, re-fill the expansion tank fully (up to the neck). Squeeze the top hose a few times, at this point the coolant should be circulating via the auxiliary pump and coolant should be seen entering the expansion bottle from the small-bore pipe into the neck of the expansion bottle. If the coolant is not circulating, squeeze the top-hose and while squashed fill the expansion tank right up to the brim, release the top-hose. Repeat until the coolant circulates.

8. Refit the cap, tighten the bleed-screw and start the engine, if the heater matrix has been drained rev the engine to 3000 RPM - this pushes the coolant through the matrix - loosen the vent-screw at regular intervals to release any air:

9. Allow the engine to reach operating temperature while ensuring the 'Low coolant' warning does not show on the instrument cluster. Only top up the fluid if the warning is shown, stop the engine when re-filling.

10. Once the engine has reached operating temperature, switch the engine off and check for any leaks. Only attempt to get the coolant level exactly right when the engine is fully cool (at least 8-hours).