What it usually turns out to be
On BMW's N5x six-cylinder engines the coolant pump is electric. 2E81 says its speed is outside tolerance, and it often comes with 2E82, "electric coolant pump, cutoff overcurrent". The pump is not visible from the top of the engine: with the lower panels off it sits on the lower right side, where its power supply and ground can be checked before it is condemned.
Replacing it properly is more than the pump. The thermostat sits right next to it and is commonly replaced in the same job after a running-hot complaint, the mounting bolts are one-time-use, BMW calls for a complete drain and refill with new long-life coolant (SI B17 01 07), premixed before it goes in (SI B17 01 06). Bleeding is a procedure the engine computer runs: battery charger connected, ignition on, heater to maximum, accelerator to the floor for 10 seconds without starting, and about 12 minutes of venting.
What gets replaced first, and why that is wrong
The pump gets replaced without its power and ground being measured — or it gets replaced alone, with the thermostat beside it left in, the old coolant reused and the system bled by guesswork.
From a documented source: Tomorrow's Technician, "BMW Electric Water Pump Replacement"; BMW SI B17 01 07 and B17 01 06.
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