Seeking Help - Hot Start Issue

I acquired a 1969 Mustang from a family member to restore. It’s automatic and the engine is a 302. Within the past 6 months I replaced the battery , ignition switch, ignition solenoid and the starter. Due to the fact that after the engine warms up the car will not restart. Dead , no crank, no clicking , nothing ! I suspect it is a hot temperature issue but don’t where to go from this point .

Appreciate all suggestions!
 
Do the battery cables look like they are from 69? The cable underneath the insulation can deteriorate ... If they look old it would not hurt to replace them..
 
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I acquired a 1969 Mustang from a family member to restore. It’s automatic and the engine is a 302. Within the past 6 months I replaced the battery , ignition switch, ignition solenoid and the starter. Due to the fact that after the engine warms up the car will not restart. Dead , no crank, no clicking , nothing ! I suspect it is a hot temperature issue but don’t where to go from this point .

Appreciate all suggestions!
I'm having the same problem with my 88. My mechanic friend measured the voltage as I started it with the hot starter and it was drawing over 500 volts. He suggested I put on a high torque starter. I haven't' gotten to it yet, so I don't know if it will work.
 
Would like to update everyone that responded to my post. The negative battery post was not grounded to the auto body. The wires from the alternator were replaced because the wires were cut had wire nut for some unknown reason. The dead restart was traced back to the ignition switch harness. One pin on the female wire harness was burned. I am waiting on a new ignition switch wire harness and fingers crossed that was the problem with the hot restart issue. Thank you all for your input.
 
I hope that you have found your answer to the hot start issue, it sounds like it. Just to throw it out there, a battery can do the same thing. I had them start and run just fine until you try to hot start it, then if you let it cool down it was fine. Replacing the battery fixed it on two different cars over the years.