Scientific or not when I shoot the temps on my tires I look for consistency. I am presuming the tire pressure charts (which I follow) have pressures listed that are proportional to the load carried and thus the amount of tire flex is constant between all tires.

Again, assuming that is the case I can expect uniform temps. If I have a tire out of the norm then further checking is necessary. I have learned the tires on the sunny side of the coach will be slightly warmer, but if I check them almost immediately after stopping the differences are only a couple of degrees.

If I have a failure of a tire on the drive axle I presume it will show up. I am not able to shoot the temperatures of the sidewalls on the inner dual, so I shoot the center of the tread on all tires to be consistent.

I agree strongly with a cold temperature check and then not adjusting pressures on warm or hot tires. That has been emphasized consistently by all tire companies. The cold inflation pressures are established knowing the pressures after driving are going to increase.