When getting a jump start, current is still going thru the same cable and cable ends. We must be sure they are good; and the extra battery is also trying to rotate the same HEAT SOAKED solenoid or starter windings if that's the case. So a jump start may still exhibit the same symptoms.
I've always mounted the ford relay on passenger inner fender, up high even with alternator. 3/8 copper pipe flattened out, makes a great jumper in that trick. As you can see the advantage is just one big cable going down into the hot hole.
If wrapping and/or shielding does not fix it, it's time to go someplace that has real good diagnostic equipment...and that's not O'Reillys.
You keep asking about why a new starter would start cold and then not start when hot. Because there could be something wrong with it's electrical quality/rebuild quality such that heat causes loss of it's "power". That's what a bad new starter may do. As Shakespeare said "beware of a reman starter". IF everything is new, we are down to blaming new parts, thermal radiation, insufficient ground or several things at once.
Every possible cause has been mentioned, so what that means is: it's up to you to test, eliminate, isolate, fabricate, investigate and retest and reinvestigate using good equipment. You are missing something/taking something for granted/false test results. Good luck and let us know what it was.
