Ron's answer was when this thread was posted in the 4.0 forum. It probably still applies
I would replace ECT(engine coolant temp) sensor first, not an expensive part.
There are two temperature devices on the engine
ECT sender, for the dash board temp gauge
ECT sensor, for the computer
Both are located on the thermostat housing on the 4.0l SOHC engine
They are not interchangeable
ECT Sensor will have Green/red striped wire, and Grey/red wire
Sender has Red/white and black/white wires
How to here on changing the thermostat housing:
https://bengrosser.com/howto/fordthermostat/
It is a common leak point for this engine, but pictures show where ECT sensor and sender are located and how they are removed, the clips that slide out
All engines need to be Choked on cold start, Fuel injection doesn't change that, but it does change the way engine is "choked"
With no Jets a choke plate can't work to suck in extra fuel need to keep cold engine running
So the computer must add the extra fuel on cold start, and keep adding it until engine warms up
And thats where the ECT sensor comes in, it tells the computer if engine is cold or warm
If ECT sensor is "telling" computer engine is warmer than it is then engine is not Choked so will be hard to keep running until it does warm up
And thats your description of the symptom