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I have a supercharged 350 small block in my 71 which is a recent install. I am now having starting problems after the engine is warm. If I shut it down it needs to be left to cool down for a long time before it will start again. When it is cold it starts fine. The starter has been replaced and also the battery. Setup is equipped with an electric cooling system and MSD ignition. When you try to start after the engine is warm it is as though the battery is low and the starter just drags.
My MSD has a cranking spark retard. Is that the way your's is? This reduces stress on the flywheel and starter during cranking for higher performance engines...
Otherwise, you might be able to insulate the starter from your headers like the others have indicated.
Check that your starter solenoid is getting 12volts when you turn the key. If not then your problem could be the keyswitch, clutch/neutral switch or associated wiring to the solenoid. You may just need to open up your solenoid and clean the contacts.