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Mike, is water pump/ thermostat part of your repertoire?

There are no relays inside the pump but there are a ton of electronics in there which have probably gone faulty. As mentioned before, the stat has no sensors or electronics so is not really capable of causing the pump to run.

Pump (Pierburg) + stat (Wahler) ordered. I'll pick up some antifreeze from BMW on Thursday - anyone know how much I'm likely to need to replace by the time I'm done?

I got a mobile ex-BMW guy out sort out my pump and stat. I gave £165 which included deleting a couple of codes. Quite an expensive episode....

keith777 wrote: ↑Mon Nov 06, 2017 11:29 pm Mike, is water pump/ thermostat part of your repertoire?

Yes, I can do that for you. Only just seen post.

Mike

Did changing the pump solve this OP?

Yes. That said, I'm not actually sure which was the culprit.

Its a huge draw so look at things that can be attached to the battery that take a large current
My moneys on starter motor or Alternator

It was definitely the water pump that simply didn't turn off regardless of whether the car was running or not. I proved this with an ammeter and by pulling the fuse. The point is I'm not sure whether the fault was with the electronics in the pump or in the separate thermostat. Both have electrical connections but I didn't bother to investigate further, I figured replacement of both was quicker and cheaper + gave more future peace of mind than diagnostics.