If you set the tire pressure at the correct pressure cold (meaning the temperature inside the tires air chamber is equal to the ambient temperature) then as long as the tire hasn’t been compromised by a foreign object, any rise in pressure will not be a problem.
As to tire temperatures, most new tires are cured between 340° - 370°. The rubber on the side of the highway most of see is a result of when the inside tire temperature reaches/exceeds the tires curing temp which reverses the vulcanizing process. All that being said, as a tire builds temp, it doesn’t take long for that tire to rise rapidly if the tire has been compromised. So temps approaching 200° should be avoided. If all tires are that high then the speed is too high for the weight being hauled. Usually though it’s just a single tire that goes that high. Which again is an indication that the particular tire may have an air loss, overweighted, or is rubbing on the suspension or trailer.