I just did a radiator replacement on my wife's 2001 4.4L. Thanks to meltdown325 for the instructions. It really helped to know about the trans cooler (heat exchanger). I have a couple of things to add to those instructions:

a), I did not have to remove the fan/clutch at all. Once the shroud & radiator are fully unhooked from everything, carefully lean the shroud back over the fan blade, towards the engine, and maneuver the radiator out. Takes a small amount of force & manipulating, but it's really not hard.
b), Just noting, the two black triangle shaped pieces over the top of the radiator are actually connected together as one long piece. Once those two outside bolts are removed, you can lift out the whole, long piece. The inner bolts appear to be just some sort of plastic adjusters, and they remain in that long piece.
c), The big silver (aluminum) block is the heat exchanger part of the trans cooler. It is clipped to another part of the trans cooler, a piece of black plastic that on first glance appears to be a part of the fan shroud, but is actually seperate. It has passageways in it for coolant to flow through. You don't have to take the heat exchanger apart from this black plastic piece. From the black plastic piece, just remove the torx screw (which meltdown 325 refers to as a bolt) from the top, and the plastic rivet from the bottom (which holds it to the radiator). You can then ease the whole trans cooler assembly back from the radiator and remove the radiator. On reassembly, clip the trans cooler to the bottom of the radiator with the plastic rivet only. Lower the shroud into place (it has a couple of long tabs which slide down into the black plastic portion of the trans cooler). Then replace the torx screw at the top of the trans cooler. Difficult if not impossible to get the shroud tabs into place if you install the torx screw first.
d) I left the top hose unhooked from the radiatior until I had installed enough coolant that it was up to the bottom of the top neck of the radiator, then hooked up the hose and continued filling the system as the engine ran. Don't know for sure, but I think this helped with the bleeding. It seems to be full, without any trapped air.

Hope this helps someone!

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2009 X5 3.0
2001 X5 4.4 - Sold