Recently, I found trainsmission fluid in my 2005 Lincoln LS Sport 3.9 V8 cooling system. What may cause this?
Your car has a transmission cooler element inside the radiator end tank. That element is leaking. If you look at the sides of the radiator you will see that on one side there is a metal tube running into the plastic end tank at the top and another metal tube at the bottom of that same end tank. These lines carry hot transmission fluid.
Somewhere inside is a leak. Generally the repair requires a new radiator. The internal transmission cooler element can be replaced on its own but that's a pretty involved repair involving bending the tabs that hold the end tank to the radiator core. With a car as old as yours a new radiator makes more sense.
I am very curious to know what caused the leak. I'm guessing you've replaced coolant from time to time using plain tap water (with anti-freeze coolant) instead of anti-freeze and distilled water only.