Multiple posters have discovered that the POSITIVE jump point is loose causing all types of issues. I would recommend, as everyone else has, remove the positive nut, cleaning all contact surfaces and reinstalling. I would also recommend removing the battery, cleaning all terminal ends and ground contacts in the trunk as any POOR negative grounds will create all kinds of electrical hell within the vehicle up to and including part failures and low voltage relays, and modules failures.

The parts under the hood have been exposed to high heat soaks, water spray, and general corrosion for the past 15 years. Give everything a wrench turn after cleaning.

Voltage drop Test listed below

And to experimentally verify that the jump port is in the circuit, I just did a quick test using my clamp ammeter on my 3.0i.

I clamped around the cable immediately to the starboard of the jump port cover.

When starting the engine, indicated current through that cable increased positively and then quickly (within about half a second) overloaded since it exceeded the 100-Amp range of my meter.

Then, following the start, while the engine was idling, current showed negative (driven by the 120A Valeo alternator, flowing back toward the battery) of 80 Amps, dropping to 60 after a few seconds, continuing to drop, which was enough to remove any doubt I may have had.

Like I said a couple of posts earlier, wiring diagrams on the internet show the 4.4i and the 3.0d having different setups (same as eachother, different vs. the 3.0i), where the jump port is at the end of the line. So in those cases, current won't flow past it except when jump starting or charging at the port.

But in the 3.0i, it's definitely in the normal path of high current. It makes perfect sense that any looseness or surface corrosion at the jump port would cause the port to get hot, and of course that should be fixed for many reasons.

Regarding the wiring diagram posted earlier, I think that branch coming off the alternator is just not there on my car. And I think the jump port is correctly indicated but mis-numbered as I suggested in that post.

Problem resolved.
 

Terminal replaced with one from a wreck.
Thanks for all of your help.
Before:
http://imgur.com/5ZrgvT7
https://imgur.com/oCGXwaf
After:
http://imgur.com/C7icxq6

X5 is back up and running. Wire is cool to touch. Battery is charging again.
Terminall was originally very corroded. When I attempted to clean the copper loop at end of wire, it disintegrated.

Sorry. I couldn't get images to load in the post.

Much better. That other cable was pretty bad. Oxidization is like a cancer and can spread. While your cable end and nut are copper, the post is still some blend of felsic metal. The potential for electrolysis and oxidizaton still exists. If you’re in an area where the DOT salts the roads or are living on the coast, consider using a dialectic grease on all your grounds, battery terminal and alternator. The grease is hydrophobic and keeps the connections from corroding. Just dab it on your finger and thumb and smear it around.