1987 rough idle in hot weather

[87TurboBird2.3]

I have a 87 Turbo Coupe (2.3L) and a 90 T-Bird LX with the 3.8L. The issue I’m needing advice about is for the 90 T-Bird. When it’s warm outside (80’s or hotter) and I shut the car off after driving it, go into the store (or wherever) and come back out and start the car the car misses, spits, sputters, and runs really rough and sometimes it dies, but fires right back up. But once I start driving it, the issue clears up right away until I stop and shut the car off and start it again. I don’t have this issue until the weather gets warmer (80’s or above). What it reminds me of is a vapor lock issue on a carbureted engine, but with this car being fuel injected, vapor locking doesn’t happen because of the high pressure fuel pump, correct????? Or am I wrong? I have no idea what’s causing this problem. Has anyone experienced this before or knows what the problem is? I’m at a loss and don’t know where to start looking. Thanks for the help guys.