My 5.4 was the oil cooler and unfortunately the part at ford is around $300. Make sure you get the cooler to oil filter adapter lines rubber "O" rings if and when you get one. I had mine tested at a radiator shop and you could see it spurting from the coolant side into the oil side even under low pressure.

Now.for the 10-20 plus flushes to get all the oil out of the engine and alternating simple green in the warm water!

The price would be because of the shop hourly rate times their hours into diagnosis plus all parts. So $300 for the part plus coolant and other materials to flush it many many times and "x" shop hours. $1300 sounds high. The cooler is above the engine crossmember on the drivers side of the engine. Its kinda a pain in the ? To get to but with patience a guy to do it yourself.