The part of the tire touching the road is flattened out by the weight it's carrying. When the tire rolls that spot isn't touching the ground anymore - it changes back to normal shape. There's always a portion in contact with the ground, so the tire is always changing shape back and forth between normal and slightly flattened out, the flat spot chasing around the circumference of the tire. Changing shape generates heat. Heat destroys tires.
Underinflation = the 'flat spot' is a lot more flat, so a lot more shape changes is taking place... therefor more heat is generated.
Driving faster makes makes the shape change at every given spot occur more frequently, so more shape changes = more heat.
So the less you're inflated and/ or the faster you drive, the worse off your tires are. The weight rating of the tire usually states "at max inflation." Less than max inflation = less load capacity, because the tire is deforming more.
I've read that normal pressure gain is 10-20%. So, an 80 PSI tire (cold) should go to 88 - 96 PSI hot. That could be very contextual (and wrong), but there's an expected pressure gain and that is part of how proper pressure is established - Google is your friend.
I run 80% Nitrogen in my tires. ;)
When a tire is mounted on a rim, it starts with air in it at ambient pressure. How do they evacuate that air before filling with Nitrogen?