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I have a 428 in a '73 F-100. When the engine warms up it will not turn over. It does fine when cold. The battery & selenoid are good & jumping does not help. I can push start it & it fires right up. I have Hooker Competition headers & think they may be heating up the starter. Does anyone make a starter heat sheild for the FE series? Do they help?
What you have is a bad starter, may have been caused by the headers, replace you starter, if you can't find a shield, just make one out of thin steel. Anythng you add will help.
You have heat damage to your starter so you need to replace it.
Your cable from the selenoid to the starter is too light.
When you replace the starter, wrap both it and the headers with header heat wrap to protect it.
I use 4ga. cable from my battery to the sel. and from the sel. to the starter. I had this problem in my '84 bronco with a 302 and I noticed my sel. smoking when I tried to start the motor when warm. I had an 8ga. cable setup so I switched them both to 4ga. and haven't had a problem since. I still have the old sel. in the Bronco so it shows you the cables were too light duty.
PS: I've got a 428 I'm going to build this winter for my '68 Mustang. It ought to be a fun ride.