2000 Crown Victoria occasionally doesn't start after warming up.Actually sounds like it's flooded when you try.Wait 15 minutes no problem like it never existed.

try the drive belts spray with wd40 or similar see if the sound changes .if so renew belt.

Your fuel pump may not be working properly

You didn't provide any sounds or anything
you may have checked so far

Did you test the battery?

Is the battery 6 years old,that you would know.

Are the cables corroded or loose?

Does the starter solenoid click,that could be bad
or the starter it's self

What about the head lights or any other power

What does work is my question
You need to come here with something
to work with

Does it work when you turn the A/C on? The fan always kicks on with the A/C, if it doesn't look for a blown fuse. Or possibly a fan motor burnt up. If it works with the A/C but doesn't when the engine is too warm, it is probably the temperature sensor.

The starter or it's solenoid

The new battery & alternator didn't
but the problem in there

Losing coolant? Might have an intake leak.

Sounds like a bad starter possibly getting non functional with heated up condition.

The solution is to change the starter with a new one, hopefully lifetime warranted if that's available.

check the air bypass valve it causes a hoot type noise

if it starts to flood it may be the coolant temp sender. it could also be the crank angle sensor. hope this helps.

The noise is from the idle speed control valve on the intake, have seen this issue many times while working for Ford, replace it.