This is our third X350, so not completely a novice.
The first was a XJR and I changed the auxiliary heat pump on it as it was not running with the ignition on engine off, the new one did run.
Now we have a 2004 XJ8 and the cabin heat on the passenger side is really good, but the driver's vents are almost cold.

Reading posts, it could be the auxiliary pump or it could be the cabin radiator.
I cannot seem to hear the pump running like I could on the XJR, but saw a post indicating that XJRs run the pump 100% of the ignition on time, with the suggestion that normally aspirated engines don't? Can anyone clarify when I should hear the pump running?

Judging by the large difference in temperature between the vents, I am thinking it is more likely to be an issue with the cabin radiator.
There is talk of flushing helping, more specifically back flushing. I could not find guidance on the best way to do that? Posts were oldish, just wondering if there are any updates.
Suggestion was not to use chemical wash on OAT based system. Would a thorough back flush with a hose, then adding chemicals work? Did anyone look at the deposits and find some mixture that dissolves them?
I guess I can work out which direction the flow to the heater goes in based on the hoses to and from?

I will keep searching the forum for now, likely order brushes anyway and aim to rebuild the pump soon (car has 85k miles on it, but also 18 years of use).

TIA for any help

 

follow the two lines running across the right side of the engine bay. blast some clr in there and flush it out with a garden hose

aux is right under the expansion tank it should run with the heater. just buy a new one they’re cheap. look up 2002 vw golf or similar