Cat 3406b won’t start when hot

Maybe check the voltage to the fuel solenoid while it is cranking. Maybe even take it off. Thank that is the one that pulls the plunger in to run. Cut the rod off of one the side of the road once and put it back on. It ran just would not shut down. Thank the A's worked opposite.
Just some thoughts as I never had that exact problem.

 

I agree with boxcar. Could be a fuel shutoff selinoid. Pull it off and see if it starts. They do go bad

 

Very strange. Can we see a picture of your truck and the side of the engine with the pump and lines?

 

Have you removed the filters after it gets hot to see if they are full? I'm not going anywhere with this, but it may lead to your problem.

 

@wore out

 

Looks good and like you have done a lot of work on that. I am at a bit of a loss never having see that.
A couple of things I would want to check is the fuel pressure on the left filter head. Would need to have a gauge plumbed into it, it is an o-ring fitting #4?
Really sounds like a injection pump problem to me but I know you have had work done on it. Kind of jack leg deal and not so simple on your engine but I will share this. It was a Lull or similar machine built on a 5000 Ford tractor. It would start misfiring on two cylinders when hot. This was a 40 mile out in the country service call. I pulled an injector and managed to connect to the injector line without bending it. Tightened it back to the pump and injector and ran the engine. It did not spray fuel. Connected to the pump on a working cylinder and if sprayed fuel. All doubts removed in the county with little to work with. An injector spraying fuel like that can push it into the skin or put an eye out. Take no changes. The engine running with an open injector hole is also quite loud.
Maybe someone else has some better ideals?