Tire pressure (temperature) increase while driving

I check our tires and wheel bearings with a laser aimed temp gun.
The tires go up about 10-15 on ours most or all of the time.
I check them when we fuel up or just stop for a while.
The right inner tire nearer exhaust is about five degrees warmer, than the rest..
I don't remember if it was especially hot some of the time or not.
Just considering sometimes, If I had the energy, about a scoop somewhere directing air between the two drive tires per side. Might be disadvantage, in Az, when temps are 115 or so.