87 mustang idle problem

change the coil coils heat up and short out

You could have a faulty engine coolant sensor or intake air temperature sensor. Fuel injectors clogged or dirty flooding engine.
Clean fuel injectors, replace fuel filter and air filter, and see if the problem persists.
If it does ECT sensor is bad. If CMP sensor was bad, the vehicle won\'t start whether cold or hot. CKP senso and CMP sensor work together if either one fails, the vehicle won\'t start. Have the vehicle code scanned.

After you kill it, when you try to start it back up, does the starter turn the motor? Or is it froze up (will not turn over)?

ENGINE FLOODING REPLACE AIR FILTER AND CLEAN FUEL INJECTORS DIRTY LEAKING FUEL INJECTORS WILL LEAK CAUSE ENGINE TO FLOOD OUT.

is the car running hot? some cooling fans never come on going down the road because the air comjng through the front of the vehicle keeps the car cool enough that it doesn't need to come on. but if it is overheating then you may want to check the cooling fan relay.

then it cuts when hot ?
when cold start is it take some time to run from clod ? if yes then injectors nozzles if not then it is the (coil) well cut off when engine is hot

Sound like you could have a defective ISC (idle speed control) sensor.

It can be anything - throttle adjustment, burnt out spark plugs, clogged fuel filter(honestly not common and really just a reason to replace it xD), or a worn out fuel pump.
First check the throttle/idle setting if it's fine, then the wires leading to the throttle body and air sensors, also the wires leading to the fuel pump.
also check if there isn't too much oil in the air filter's box or anywhere the engine vent's hoses lead.

the black smoke means that it is buring the gas to rich.

I don't know the model year? Key on engine off, use a gage and check proper fuel pressure. Then with key off, see if pressure holds for a bit? If it drops like a rock, check for a fuel pressure leak. If the engine is hot and trying to flood for some reason, your going to have a tough time. Any applicable trouble codes? Check your coolant temp sensor, only if testing leads in that direction.
Smell of your crankcase oil dipstick, does it smell like gas?