If it is your oil cooler, IMO likely:
I have been told by a Ford Tech at the dealership that the new Ford oil coolers are upgraded, with bigger passages... But a couple of the Techs here on FTE have called BS on that info... So I really don't know if it is true or not.
There is a lot of information on this issue on this forum. Do a search on the 6.0 Forum and read up on topics like "EGR", "Oil Cooler", "EGR delete", "Bullet Proof EGR Cooler" and spend some time reading the threads. There are a few different schools of thought on this issue so read up and make your own mind up on which way you want to go. I think everyone agrees, however, that a coolant filter is a VERY good idea, so I would definitely order up one of those and install it as soon as you get the oil cooler replaced. While the oil cooler is being replaced, that is the time you will want to either replace the EGR cooler with a stock EGR cooler, a Bullet Proof EGR Cooler, or delete it all together and block off the EGR passage. Like I said, there are a few different schools of thought on this issue. When the top of the engine is exposed, you will want to deal with both coolers at that time as the labor is the expensive part of accessing the area for both.
One caveat, if deleting the EGR, understand that it is illegal in the US. Not sure about requirements in your neck of the woods. That option is one that you will have to consider carefully. Many folks on this site feel that an EGR delete is not the way to go, but do your research and decide for yourself.
Good luck, Tim