Tire pressure when traveling

Tires warm up when rolling due to friction and internal flexing and such, and the air pressure in them increases in accordance with the gas laws. If the cold inflation pressure is correct for the weight on the tires (which implies that they aren't overloaded), there's nothing to worry about. Indeed, that's the main reason why tire pressures are measured and checked with the tires cold: the readings change with the temperature, and it's practically impossible to reliably get the same operating conditions to check them warm. Also, since underinflated tires run warmer than properly inflated tires at speed, it's possible at times for underinflated tires to have a higher warm pressure than properly inflated ones.

The (cold) pressure will change somewhat due to changes in ambient temperature, and should of course be adjusted as necessary to compensate.