also a test of the ect should be performed.
Before you start the car note the ambient temps surrounding the engine using a thermometer. This will give you a pretty good idea of what you coolant temp is cold before starting. using the chart in the link take a reading of your ect . say if the ambient temp is 75 you should get a ohm reading of between 24.27k-37.30k +/- 15%
Or a voltage reading depending on how you test. Of between 2.62v-3.06v
If the ambient temp of your cold engine is 75 any your getting a reading showing much colder then it is reporting to the ecu a false temp.
A lot of times the ect will report a temp of -40 degrees and this will cause the ecu to widen the pulse of the injectors dumping so much fuel that the engine struggle to stay alive.
A false reading of too hot will have the opposite effect causeing a very lean condition and you may get popping and back firing.
Some times the ect when cold will report a very cold reading then as it warms up it will report a very high reading.
An egr valve that is stuck open can cause the engine to stumble at idle also.