I recently had this same issue. Truck would run real rough when I started it an until I got it warmed up and driving for about 15 minutes it wouldnt run right. Felt like it was missing and was low on power. The engine light also came on whenever this was going on. I had my mechanic pull the codes for me and it was the p1316 code. That is an idm code. First thing that always comes to mind is the under valve cover harness. UVCH. It is under the valve over on each side and plugs into the injectors. They are known to come loose over time and the connection is broken because of the rough idling of a cold engine. I started my truck and paid attention to the exhaust manifolds, see if it seems like on side of the engine is vibrating more than the other and then touch the manifolds before they get real hot to see which one is warmer. My passenger side had much more vibration and was cooler than the driver side. I pulled the valve cover, pretty easy to do, and the harness was halfway unplugged. The clip was broken so I bought one from ford for 80 bucks. I can get you a link to the same thing online for around 60, i dont have the link right now. This sounds to me like it is your problem but you wont know til you look. Its free to pull the valve covers and take a look, only takes a couple hours. Let me know if you have any questions.