I got my son an automatic 2005 Mustang with 150,000 miles & he loves it. However, on HOT days it doesn't want to start. It's a black car with a black interior. At his job he parks in the sun. He opens the doors & lets the interior cool off for about ten minutes, then it starts. After a few days of this the battery was dead. I bought a new one. Today it happened again. It only happens on really hot days. Short of cutting vents in the hood, do you have advise?
Any codes? Does it crank but not fire up? You can spray a little starting fluid into the intake to determine whether the problem is spark or fuel. If it fires briefly on starting fluid you have spark, so the problem would be fuel delivery. If the engine doesn't fire then you have no spark.
Crank sensors can be sensitive to high temperature when they start to fail. You could try spraying it with some CRC freeze spray to see if it starts working.
EDIT: I didn't catch reading your post the first time that the car starts when the interior of the car cools off. That indicates a possible problem with a computer module inside the car failing in high temperature. For the battery problem you'd need to diagnose the charging system and check for parasitic draw.
I wonder if a code scan would catch a computer module fault. I guess I'll find out tomorrow.
When you say it does not start, when you turn the key to the ON position, do the lights on the dash light up?
Everything powers up, but weakly - as if the battery is dead. The horn barely even sounds... then after the interior cools off because the doors are open for 5 to 10 minutes - everything works fine.