Warmer than you'd think it would be. I only had to be at 130ish for mine to die. Easily capable of being there in 15 minutes of run time. If your temp gauge reaches a normal operating temp, you're already at or over 141*.
Honestly I doubt it's your idm or even injector solenoid related. The idm usually has some symptoms related before it just stops working, same with injector solenoids. They don't just all die at once and cause a no start, also very rare to have one go bad.
Your harbor freight scanner won't do much unfortunately. You need something that will give realtime data with the ability to look at different parameters at once. The first and least expensive option that comes to mind currently is going to be the forscan smartphone app or download it on a computer. Or there is a couple of others that are free that you can download on your phone And you will need a Bluetooth OBDII adapter for a phone. The adapters cost about $5 on amazon depending on which one you get. If using a laptop you'll need a USB to OBDII cable for the forscan app. I'd do one of the free phone apps and a Bluetooth adaptor if you have an android or iPhone.
The IPR is quite far down into the valley of the engine, it comes out of the back of the hpop toward the driver side of the hpop. Easiest way to know exactly which it is, is to google for a picture of it. You should be able to see the wires going into the solenoid, then behind that would be a spacer and a tin nut holding the solenoid and spacer on. If the tin nut or any other 1/2"x20 nut is not on there, that is a problem.
Also, I do not remember if it has been mention but is there oil in your icp sensor connector? If there is this is also bad and you need a new one. Try starting it with the icp sensor wires unplugged and see if it starts. If it does fire, your issue is the icp sensor. (Reread and noticed this was mentioned and tried. But you still need a new one since it's full of oil. Memory says it's around $100-$120 maybe.)
Once you get a device to read data in real time, what we need to know is what your icp sensor is reading, as well as ipr duty cycle, both while cranking. Once we know this we know if it's hpo related or not which narrows down or rules out a decent chunk of things to check. It's very hard to diagnose an issue on these trucks in person without some sort of a device to monitor what the truck is seeing, no less trying to do it over the internet. That prevents you from just throwing money at it.
Fuse diagram would be in your owners manual as well as a list of what each fuse does. There's also copies of the owners manual online if you google "xxxx Ford F-250 owners manual"( insert model year where the xxxx is.) I was able to find one year specific to my truck and download it to my phone as a PDF file.