I hope you meant 125F, not 1250F.
My logic is a bit different. The over pressure device is there for a reason, specifically to prevent catastrophic failure. Excess stress occurs BEFORE catastrophic failure.
If you are even approaching the trigger point for these disk (like you can by heating a very full tank to over 125F) then you have significantly exceeded the design pressure, even if you don't actually rupture the disk. This causes excess stress and excess stress, repeated many times will shorten the life of a structural object made of AL. I would suggest this is very similar to the stress from fast fills or over filling AL tanks. Not the end of the world, but something that I choose to avoid if possible.
Confession: Last week I left a tank in the back of my SUV and my son closed the hatch while I was diving. When he hooked up the tank for the next dive he noted it was at 3400PSI. If was not even a hot day by Texas standards.
This may be a minor point, but the terminology is not quite correct. There is a difference between the working pressure and the design pressure. The hydro is done to 150% of working pressure (3000 psi working, 4500 psi hydro). Design pressure is higher than either of these, since the cylinder is intended to have a periodic hydro.
You are correct that the cylinder is pressurized above its working pressure. I'm not sure if this stress actually changes the life, or if it is so far below the yield strength that it is insignificant. Certainly operating frequently above the working pressure is something the manufacturer would advise against.