Yesterday I was on a DH track for the first time. I have Avid Elixir 7 brakes with 203" rotor in front and 180" rear. The descent took about 5 minutes, and the ropeway up about 15 minutes. After 6 runs I started to notice that my brakes refuse to work properly, and on the 9th and 10th run they were almost gone towards the end of the trail. On the first two runs I used them a lot, because I didn't know the trail, but it surprised me then when I stopped using them excessively, they started to fail me. From here comes the question, how much time takes them to cool down? I understand 20 minutes pause from the runs doesn't helps much, although the rotors were cold. Guess DOT keeps it's temperature for more time.
It may not be the temperature of the rotors at all. As @cmannett85 mentioned the rotors will cool very fast, much more likely that the pads are starting to glaze over which reduces their coefficient of friction substantially. This will make it feel like your brakes are 'fading'. Hot calipers aren't your problem - the pad-rotor interface is what matters. It's very unlikely that you're overheating your DOT fluid.
In my experience, when you are repeating downhill runs (or on a trail with any extended braking periods) you may need to change your brake pads for a different type.
I had huge problems years ago with the pads I used to use until I switched to sintered metal based pads. They perform much better over the course of a whole day than the old organic pads.
There's probably a little of the 'you get what you pay for' with brake pads.
The rotors cool very quickly (under 30 seconds for glove-meltingly hot to ambient). But the caliper can hold heat for some time, I'm very surprised at your 20min claim though - there's so little thermal mass. Modern disc brakes use an 'open' system which involves a reservoir with a metal diaphragm in, so when the fluid gets hot and begins to expand, the diaphragm expands rather than the pistons close. However this will only work to a certain point, after that your brakes will 'fade'.
In my experience this usually boils down to the rider feathering the brake, i.e. letting the pad lightly touch the surface - not enough to slow you down noticeably, but enough to gradually generate a huge amount of heat over the course of a run. You'll be doing this without realising, I did, for years!
Often it can be helped a lot by adjusting the lever: Lessen the lever reach and shorten the bite point. This will have the effect of lessening the modulation (which you don't need much of in DH) and lowering how far your brake finger (one finger for DH, you need the rest to hold on) has to reach to rest on the lever. The latter point has a big psychological effect because your hand is closer to being a fist and therefore feels like you have more grip - it's hard to grip a bar hard with an outstretched index finger, your body naturally wants to pull it in.
If however, you get to the point where your brakes have faded, you will have to compensate for the larger fluid volume. To do this you will have slacken the bite point off until it feels the same as it did.