Thank you very much for your input! The temp sender is on the water pump. It's a four-contact sensor. There is a second one in the lower hose at the radiator. That one, I believe from what I have read, controls the electric fan. I was able to do an active test with it using my scan tool, and it works. One experiment I wanted to do was an active test with the engine running, but with the engine on I can trigger it, but it turns off after a few seconds. As far as bleeding it goes, the procedure is simply to turn on the auxiliary water pump for some period of time. I don't think mine works...nothing happens either by triggering it with the heater controls or with the scan tool. I have one of those +the hoses on the way as well.

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2003 BMW E53 X5 4.4