Rear differential noise - thoughts?

Hi all,

It appears that there is something wrong with the rear differential in my car. It's a 2004 Hyundai Santa Fe, 3.5l, 4wd.

When the car is warm and has been driving down the highway for 30-45 minutes, a "clunking" will begin to happen in the rear differential. I know this because I had it up on a lift at a local shop and we were able to hear the clunking coming from the rear diff while under power.

It's a single "clunk" that happens every 3-4 seconds, but the timing will vary based on how fast or slow the car is going. As you're driving down the road, you can feel the entire car jerk when it happens. After 30-45 minutes of highway driving, you can feel it happen at low speeds, but the longer you drive the car, the more frequent and violent it gets. (after 3 hours of driving, it was a consistent 2-3 second interval jerk that rocked the car pretty good at 40 mph)

The weird thing is that when the car sits and cools off for a while (30 minutes in a parking lot or so) the issue instantly clears up. You don't feel any more jerking until the car gets hot again from highway driving.

We put some limited-slip differential lube in the rear diff (whale sperm, as the mechanic called it) and it seemed to help a little bit, but the problem still persists.

I don't want to swap the rear diff unless I know for sure that's the only way of fixing the issue - anybody have any ideas?