It sounds like the "coolant bypass hose", but nothing on mine was painted on that side of the engine, it was just black rubber, so I'm not sure that's what you're talking about. To be sure, The upper radiator hose stops at the thermostat housing in the block. From there, coolant runs through a slightly smaller diameter line down the drivers side of the block into a "Tee". One branch of the "Tee" connects to the back of the cylinder head, while the other runs behind the head, and then up the passenger side of the engine (between the block and exhaust manifold) and then cuts over to the coolant resevoir on the passenger fender. Is that the part you're talking about?
If so, Its a dealer only part commonly called the coolant bypass hose, but I'm not sure if that's the official Ford name for it. You can see it pictured in the lower left of this drawing labeled 8C633:
http://farm3.static.flickr.com/2683/4169865671_e226c978a6.jpg
Mine recently ruptured, and it's a major pain to replace. The exhaust manifold must be removed, and pulling the intake manifold off makes it much easier to remove and replace everything from the back of the cylinder head. The part cost is around $100. The shop I had look at it quoted me $900+ because of all the labor involved. It took me a day and a half.