Yet another tire pressure question.

[JOglesby]

I've read so many posts about tire pressure but can't seem to find the answer.

SO here it goes. I currently have ST205 75R14 load rating D tires on my Keystone Bullet. The sticker on the camper and the markings on the tires say 65 PSI, max 65PSI cold. This is where I start. I am religious about checking the pressure before I tow. We also have a TPMS. My question is, assuming the trailer is fully loaded (7,600 pounds) and I have inflated to 65 psi when cold, what pressure should I be worried about while towing and they have heated up?

I see a pretty rapid rise to 69 PSI within the first 10 miles or so. I have my TPMS set to warn me at 77 PSI, is this to high?