Ok, first off, it sounds like you have a defective positive battery cable.
Not that it would cause a short, but that it can't handle the loads put on it.
That would explain both the heat and the fact that everything dies after you hear the relay click.
It won't however, explain any of the other symptoms. We're just trying to eliminate it anyway, if there's more than one thing going on.
I suppose that if you have a short through the starter relay it could stop the power, as
Timmy390 was saying, but only a few other things can kill power to the rest of the truck. Those are:
1. The main positive battery cable. Just get a new one and be done with it. Cheap insurance. Might as well get a new negative too, while you're at it. Less than 15 bucks and you can at least eliminate them from the list.
2. The main negative cable, but you said you replaced that I think? Or was it just the starter cable?
3. The fusible link there at the relay that feed battery power to the rest of the truck.
They can fail partially, but usually once they're blown, nothing works after that.
The ignition coil can't do any of these things, so it sounds like you now have a trail spare.
The starter can cause the click, the hot wire, and a few other things, but it can't kill the power to the rest of the truck.
Another test though, is to disconnect the starter cable from the relay and try again. If it still does it, then you know it's not your starter causing excessive current to be drawn through the cable.
Disconnect the little Brown wire on the "I" terminal to the right of the relay, and that will eliminate any direct connection between the ignition coil and the starting system.
All ignition coils get hot when the engine is running or the key is left on. But the only way for that coil to have gotten hot would be if the key was on, the relay was bad and sending power up the Brown wire, or the ignition switch is failing.
Give those few ideas some time in the light of day and see what you can narrow down.
It's not uncommon any more to get a bad starter relay right out of the box. In fact, it's VERY common unfortunately.
So don't rule that out completely yet either.
Good luck.
Paul