Last summer did the chains, tensioners and slides on the wifes 2000 S-Type with 4.0. Immediately after repair I was fighting overheat issues. To make a long story short, the electric aux coolant pump had no power (didn't realize it because it was 90 degrees out when I was bleeding the system)

I have seen a bunch of topics on bleeding the systems on these 4.0's...

Bottom line - After a complete coolant drain, fill through T-Stat stand pipe with exp tank cap off, run the motor up to temp with heat set to max - 2000 RPM, (verify electric aux pump is indeed working), - If it is not circulating coolant you WILL NOT GET ALL AIR FROM SYSTEM OUT - YOU WILL EXPERIENCE INTERMEDIATE OVERHEAT with these 4.0's

Hope this helps