When hot (not overheated) if I shut the engine off it will not start again until it cools to some as of yet unknown and or arbitrary temp.
(We ended up involuntarily parked in Mitchell SD for 2hrs waiting for it to want to start again...)
The battery is good, all accessories power up, the fuel pump activates properly when the key is turned to "on", but the solenoid won't click over - at all - until it does

I've got an OBD reader and it's not throwing any codes except for the stuffy Cat - which shouldn't have anything to do with it.
Any ideas before I start throwing money at swapping parts?