Re: 07 F-150 rough idle
There is a problem but those who are looking at it are not investigating deep enough.
This may be a bit deep but when you turn the ignition switch to Run, the PCM looks at the values of the main tempersture sensors to determine it is to be a cold start by their values.
This sets the idle air opening, a richer amount of fuel and sets ignition timing.
If this sequence has a failure or out of spec sensor or action, the idle will have an issue especially in cold temps.
To go on, the reason is smooths out is when the OX sensors take over fuel control and the coolant temp begins to rise then the motor runs smooth as it should.
Certainly after the motor gets warm the cold start sequence values are "not the same" but is still looked at the same way upon ignition switch RUN position where it sees the sensors at a warmer resistance so the conditions 'set' for start are not the same.
What a good tech needs to do is take his scanner and look at the sensors under cold start conditions and compare with factory info.
If you cannot find a shop that can and will do it then it's a sad day for you and shop compentency.
You came here to ask, now you have some idea what's supposed to go on and how it can be looked at.