I have a 2002 f150 screw fx4 with 5.4 I'm getting the p0125 code which is insufficient coolant temp for closed fuel loop My temp gauge also runs a bit on the cool side on colder days and on warmer days it runs in the normal range I just replaced the radiator for a two row version changed thermostat also flushed motor and replaced the cylinder head temp sensor (CHT) all at the same time and yes I got all the air out of the system I thought I possibly had a defective thermostat right out of the box but my heater works great it actually works better now than it did before I did all this could it still possibly b the thermostat or that the CHT is defective all of a sudden and I hope not that was a bit of a chore to get to that thing any help on we're to check next would b greatly appreciated and sorry for the long post

 

From your work and discription, you got youself into a slow warmup time causing the 125 code plus the tendency to run cool which aggravates the situation even more.
The PCM program is equipped with a wamup timer.
Here in short is how it works;
For a tyical 195 thermostat operating temperature minus 20 degrees equals 175 drgrees.
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The PCM timer can run as long as 800 seconds (about 13 minutes 800/60) from a cold start 'depending' on the ambient starting temperature, waiting for the min 175 degrees as registered by the CHT sensor.
If the CHT resistance does not indicate the 175 temperature after the time period dictated by the conditions, the code is set.
The temp is program updated for every two degrees rise.
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There you have the basis for the code.
1. Is the thermostat at least 195?
2. Is the CHT sensor within tolerance for operating resistance?
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A larger radiator capacity should not be a cause of this condition.
What happens with a larger cooling capacity is the thermostat just opens and closes more often in time such that the thermostat is in control of engine temperature, not the radiator, within normal sizeing and correct thermostat operating temperature.
The thermostat is located at the 'outlet' end of the engine cooling loop so dictates the average coolant temperature within the engine by gating the coolant flow.
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First thing I would do to get a lead on the warmup curve and time is to use a good Scanner to look at the live data for engine temperature from a cold start vs time, gage reading and code setting, assuming you clear the code before the testing.
Depending on what you see for the decision as to what the issue is.
It seems it's one or even both the thermostat and CHT being out of tolerence by mistake or mfger tolerence being out of spec.
There is not much else to work with other than the coolant level being air locked and fooling the CHT by hanging it in a coolant free space.
Make sure the thermostat has at least a 1/8" bleed hole in it's outer rim area.
Let us know what you find to solve the issue.
Good luck.

 

Replace the thermostat with a a new Motorcraft unit and be done with it. Your old one is "lazy" and isn't closing and opening properly.