why would a 1965 mustang with inline 6 start up fine when cold, but then die when warm and parked for a few minutes?

It sounds like your carb is starving for fuel. Check your fuel pump and make sure it is pumping fuel into your carb. Also check your floats and fuel level in the carb. Make sure your floats aren't obstructed internally and calibrated for correct fuel level in bowl and last check your jets. May not be calibrated from box or may have gotten plugged from old or bad gas (Varnish buildup using old gas). Hope these suggestions help. I had the same trouble on my 77 Thunderbird. Bad gas. Ended up tearing Holley carb apart and, cleaning everything, and recalibrating it from scratch. Also changed mechanical fuel pump at engine block. I should switch to an electric fuel pump.