Changes in Air Temp and Tire PSI

If airing up tires to 80 PSI (Manufacturer recommended Max cold pressure indicated on tire) while air temp is 45 degrees and then traveling to a warm climate, will I likely have to let some air out? What I'm getting at is this....I start out with air temps at 45 degrees, tires at 80 PSI. I travel to where the air temp is 80 degrees. From past experience here in the Northeast, I know that my tire PSI in the summer when traveling gets to near 100 PSI when air temps are in the 80's and remain around that temperature for the duration of my trip. But now, I'll be airing up tires to 80 PSI and going from a cool air temperature to a warm temperature along with hot tires from traveling. From what I've read, tire pressure increases about 2% for each 10 degree increase in temperature. Using that as a guide, my tire pressure will be in the neighborhood of 105-110 PSI. Should I start out at something less than 80 PSI or is this something I shouldn't be overly concerned with?