Tire blowout on long descent
The ideal gas law PV=nRT can be used to work out the increase in pressure, as there's no room for the air to expand/escape. Let's try some numbers. If pumped to 100psi at 17&deg;C (290K) then heated to match a metal rim hot to the touch at 57&deg;C (330K) the pressure would get to 114psi. The tyre should be able to handle that even if rated to 100psi. Even starting at 7&deg;C and going to 77&deg;C only gets you 125psi. Altitude adds a tiny bit to this if you pumped up at sea level - around 5psi for a 3000m pass. 

Here's a plot of pressure vs. temperature assuming you pumped your tyres up at 0&deg;C and ignoring altitude.  The upper limit of the graph is approximately when your tyres and brake pads would be smoking; you couldn't get that hot because the pads would misbehave long before that.



Heat also softens the rubber, making it more likely to fail, but it sounds like you should have been within sensible limits. 

I've blown out a sidewall like this because of a sticking pressure gauge. A subsequent test suggested I'd put about 50% more in than I should have. If you'd overpressurised the tyre a little, then the heating could have taken it over the edge.

Maybe it's going too far for you, but randoneuring I carry a spare tyre. A boot is all very well sometimes, but I've seen a few tyres fail like this one and that won't go back together with a boot.

Long steady braking is sometimes unavoidable, but causes problems (including my own recent crash*). If you can, it's better to let the speed get up a bit then brake just before each bend or when otherwise needed. Spreading the heat between both brakes is also a good idea. 



* I was on disc brakes. The resin holding the ceramic together in my rear pads melted, one of the front pads jammed in a wrong position and only engaged the rotor with one edge.  This may have been due to heat as well.  This all happened when I released the brakes to allow them to cool on a long steep straight descent.