yes
You're loosing residual fuel pressure or failing to get cold start enrichment/throttle angle commanded by the PCM. When you shut the thing off, fuel pressure should stay in the injector manifolds/lines from the pump so that you don't have to prime it next time you start the truck. It sounds like it's bleeding off ifor the ECT isn't reading correctly.
You need to get a scan tool on it and check if the engine coolant temp sensor is reading correctly when the engine is cold and you are having the starting problem.
You should have a shraeder valve somewhere on the injector manifold...in the morning before you start the truck, press the pin and see if there is any fuel pressure...if not, you've got a bad check valve in the pump or a leaking regulator or injector.
If it's a leaking injector...the easiest backyard way to probably figure this out is to crank it for about 10 seconds or so and then stop and pull all the plugs....the wet plug is in the hole with the leaky injector.
If it's under ex. warranty, bring it in to the dealer and let them deal with it. That's what warranties are for.
