[Mr Jody]

I have heard of problems with a starter getting overheated by the exhaust manifold or header and not being able to turn the engine. In most any electrical conductor, increased temperature causes increased resistance. So if the starter gets too hot, the increased internal resistance will make it not pass enough current to turn the engine.

Or, perhaps the heat, now combined with some additional problem (high engine temp., loose connection etc.) may be just enough to cause the insufficient current to start the car when hot. You may want to just do a hand check of the starter for high temp if/when it happens again.

I don't recall hearing where this has been a common problem in Cobras, but in the close confines of some engine bays, it may be necessary to install some sort of shield between the header and starter.

A second thought: Have you checked the timing? When advanced too much, won't this put additional load on the starter? Since you are also having problems with operation at idle after the engine warms up, could it be that something is going on with the timing such that after the engine warms up, the advance function is not allowing the timing to return to normal idle advance, causing the problem to just feed on itself until stopped long enough for everything to cool back down? (I maybe grasping at straws, but just thinking out loud.)