99% of the time with a 6.0, if you have a no start when warm issue, it is because there is a leak someplace in the high pressure oil system.
The high pressure oil pump is located in the valley of the engine under the turbo. 2005 and 2006 engines have a stc (snap to connect) fitting between the pump and the oil rails that is prone to leaking. There is a repair kit from Ford that adds a bracket across this fitting to secure the connection.
I am not sure of the best way to locate where the leak is on the newer 6.0s. However, on my 03, there was a plug in the oil rail that you could remove. Then you could use a rubber tipped air gun pressed against the plug hole in the oil rail to pressurize the system. However, I know the design of the oil rails changed a bit between different years of the 6.0, so I don't know if the same can be done on the newer oil rails.
O-rings in the stc fitting and in the oil rail to injector connections are also possible failure points. I would bet that one of these o-rings is what failed in the example stated above.
There is a minimum pressure that is required for the injectors to fire. When oil warms, it thins out, and so the amount of oil flowing through a leak increases. That's the reason for the no start when warm condition.