Runs good until warm

year/make/model helps greatly!! Most problems with scan tool connections at diagnostic plugs are lack of power at the plug. The power normally comes from the lighter fuse. If the lighter is not working, suspect no power to plug. I wouldn't toss parts at the vehicle until you get a heads up from a diagnostic scan and retrieve any codes that may pertain to your issue

Could be bad ignition module as they have a low rpm section and a high rpm section. Low side may be failing as it heats up. Hard to test for this as parts store testers may not see the problem.

Check the EGR valve. Look up on the internet where on your car it is located. Find the vacuum line connected to it. Start the engine cold and as it warms up and starts to miss and stumble, pull off the vacuum line from the EGR. If the car idles fine, replace the EGR. Ignition system problems are more likely to occur at idle or lower rpm. Besides, testing the EGR is free, easy and do fail in high mileage vehicles.

yes you hit the nail right on the head there,, its the tem sensor playing you up, its telling the car's computer its warm when its still cold and it cuts back the fule like pushing in the choke,,, this causes the engine to miss fire and lack power till its warm change the sensor

fuel pump may be going bad have pressure tested on vehicle when warm also egr valve may be going bad or has bad carbon build up lack of power a miss will give u a trouble code[check engine] as well as egr valve and other emission parts but fuel pump usually does not

Running on a stand is not the same as running under power...In the water, you are essentially running on a dynomometer (dyno is a big water brake) If you can prove that the module isn't putting in enough advance, it would be doing the same thing that I mentioned with the damper, only for a different reason. So...you're likely on the right track. (rather have a points setup out on the water...anything goes wrong, you fix it without a tow!!!!)
Good luck

check engine coolant temperature when it gets warmer, or at operating temperature, and verify that the temperature gauge is showing warmed up to operating temperature. If the coolant temperature sensor tells the computer the engine is cold it will over fuel and miss and the engine will die. When cooled down it will run fine until it warms up. Also could be coil if it starts missing after warmed up.

HAVE THE CATALYTIC CONVERTER CHECKED FOR BEING PLUGGED.

it almost sounds like the timing is off causing it to load up on fuel.

then you need to check your timing