warmed up, hard re-starting on hot days

have have the following mustang:
2003 v6 3.8 liter, it has 214,000 miles on it. i have no error codes. if the car has not been started for 3 or 4 hours it always starts right up, it doesn't matter how hot or cold it is outside. but if i start the car and drive it until its warmed up then stop the engine for the next 15 minutes or so the car is really hard to start. so like if the car is warmed up and i stop to get gas its really hard to get it to start again after i fill up. i've noticed that if its hot outside then this problem is alot more likely to occur. does anyone have an idea what could be causing this ?
 
First thing I can think of is a bad temperature sensor. If you know of anyone with a scan tool, they should be able to check it's operation. It may be telling your ECU that the engine is cold and flooding it when you try to restart which would definitely cause a hard start condition. Will it restart if you floor the gas pedal when this happens?
 
okay i ran the car around town according to my scanner engine temp got up to 188. i bought the car back home and let it sit for 3 or 4 minutes. i turned on the ignition and got the live data going on my scanner, the engine temp reading was 192. the car started right up. it should be noted that todays weather is nothing like yesterday, yesterday was 92 degrees, today 57.
 
i don't believe so, their have been many times when i've gone to the gas station and filled it up, after that i have issues getting it to start. i'm not sure about when the tank is low, i've never thought to look at the gas gauge when i'm having problems starting it. scanner is reporting fuel pressure at 38 psi.
 
Reason I ask that is evap purge. If you top off a tank some fuel might get sucked into the evap lines and make the engine very rich and prevent restart.

So trying to determine if this was related to evap purge/fuel being sucked in, or possible a temp sensor. Either cylinder head temp or intake air temp.

V6 mustangs don’t have a coolant sensor, they take cylinder head temp instead.
 
is there any test i can do that could help you determine if its the evap purge system ? can i temporally disconnect it and see if the problem goes away ? also scanner was showing me the intake air temperature. 80 degrees, thats with the car idling after running it around town, when i'm driving it it shows 60 or so. today the outside temp was around 57.
 
Easiest thing is to just avoid topping the tank off and drive and see if the issue repeats. If it’s refusing to start with half a tank of gas, it’s likely not the purge.

Direct test would be to remove it and blow through it and test it with a 9v battery for operation. No power, no Flow should pass. Power should open it. It’s located in the pass side inner fender

View: https://youtu.be/LRga_PyeyKc?si=W7QEkR_XcN6yCV1U
 
okay thanks, i'll need to wait for it to warm up outside before i can go further, i'll get back with you when it does. the car always starts, its just embarrassing. at the gas pump, everyone just standing around filling up their cars and watching the guy with the old mustang trying to get it to start.