Great discussion!!

SAAMI specs for pressure are similar for the cartidges noted.I feel this relates to max pressures sustained by quality brass and specific cartridge design.The pressure measurements I referred to above are from the accurate reloading data tables.They pushed the cartridges to the desired velocities noted and got those pressures.

Per Hornady's reloading text Hornady performs their all ballistic work with SAAMI guidelines at 70 degrees F.All powders generally develop higher pressures at higher ambient temperatures.Personally, I would be very concerned taking a max safe 416 Rem load at 62,000 psi at 70 degrees F and hunting it at 110-120 degrees F for dangerous game in Africa.Yes you may be fine but your pressures are higher and you would seem to be at risk for big problems too.

The only way to resolve the question would be to shoot your factory loads or handloads at 120 degrees and note the velocity change/pressures involved.I think I do recall that a bullet or gun powder manufacturor was looking at that issue for the same reasons.

As for me I will stick to the 416 Rigby.More powder, more recoil,but lower pressures at higher African hunting temps.
I would have no problems hunting the 416 in Alaska with its lower temps.Cause thats where I hope to take my 416 Rem hunting Brown Bear in the future!!!