I am running OEM Bridgestone 15" and have them at 38F/36R goning on a long road trip not sure if pumping them up with Hot summer days and all highway driving is good for the tire it self?
You pressurize the tyres when "cold", ie. before you drive, after they cool off for a few hours. What we are talking about here is the volume of air you are running in the tyre, not the pressure. You are gauging the volume by the pressure. Once you start driving the tyre pressure goes up as the tyre heats up. Don't let that pressure value worry you. It's the cold pressure that is the measure of air volume we have to use, as most of us can't measure the temperature and do the math to figure out the volume at "driving" temperatures. It's a complex relationship between volume, temperature, and pressure. If you start out with more volume the tyres will heat up a bit less, and the hot running pressure will be lower than if you had started out with a much lower pressure (volume). Many are using the tyre pressures we learned on the GII Prius. I run 40Front and 38 Rear, just like I did with Pearl. Pearl S rids a little rougher at those higher pressures, but it's a little safer with a bit higher volume of air. I have to worry less about slow loss of air for example, and tyre damage caused by the tyre being "pinched" when I hit a road irregularity is slightly less likely.
Definition: Volume is the quantity of three-dimensional space occupied by a liquid, solid, or gas. The volume refers to the tire volume (the space inside the tire) which basically does not change. Otherwise as you added air the tire would balloon out. Therefore the volume remains constant; it is the pressure and temperature that change with adding air to the tire. Due to friction, the air inside the tire increases while driving. Tires are rated to handle certain air pressure... volume remains constant.
Volume of air at STP (standard temperature and pressure), aka 20C and sea level pressure is what I was referring to. Higher volume equates to more air. As you said, the volume in the tyre doesn't change much (though it does change a bit).
You can use pretty much what you like between recommended and the max pressures listed on the sidewall. As long as you are in that range you are OK. For safety you shouldn't go below the recommended pressures. I use 40 in all 4, maybe a little less in winter. I think the 2 psi difference front/rear is not needed and is probably based on a car with nothing in the back, i.e. no luggage, no tools, no groceries, etc, so I have always ignored it.
In winter with Michelin X-Ice 195/65R15 I'll use around 44 psi. In summer with the stock Michelin Pilot 215/45R17 I set lower, around 36 psi. The low profile 17" ride gets to rough for me, at higher pressure, and the mileage doesn't seem to suffer, 36 vs 40. I like to keep to keep fronts and rear at the same pressure, mainly to avoid having to adjust them when rotating.