I suppose I could attempt the math...

Aluminium has an SHC of 0.897 J/gK according to Wikipedia.

A rim weighs about 500g. So how much energy to raise its temperature
from 20C to 100C, on the assumption that 100C is very hot for a bicycle
rim (is that figure about right?)

    500 * 0.897 * 80 = 35880J

So 35880J can be soaked up in the rim before it gets to 100C. That
corresponds to what change in speed of a 100kg bike+rider?

    E = 0.5*m*v^2
    sqrt(2E/m) = v
    sqrt((2 * 35880) / 100) = 27m/s, or 97kph.

This seems to be saying that even if the rim doesn't manage to lose
_anything_ to the air, you can still brake to a stop from 97kph (using
only one brake) and not get the rim hotter than 100C.

Of course this is cumulative, so ten 10kph retardations, with no loss to
the air, would cause the same buildup.

I think this probably explains why dissipation to the air isn't terribly
significant for one-off emergency stops, but is for repeated braking
during a long descent.

Anyway, I couldn't see steel's SHC on Wikipedia but some other website
suggested it might be around 0.5 J/gK but it depends on the kind of
steel. A disk weighs around 170g.

    170 * 0.5 * 80 = 6800J
    sqrt((2 * 6800) / 100) = 12m/s or 43kph

So quite a bit worse it would seem. That's only four 10kph retardations
before the disk reaches 100C (assuming zero dissipation to the air).

I'm starting to wonder why disk overheating isn't a big problem with the
lower heat capacity and probably lower dissipation rate to the air.
Perhaps the operating temperature range of a disk is higher as I
suggested earlier. I pulled this figure of 100C out of the air as "high"
for a rim brake, but perhaps they don't really get that hot. A disk on
the other hand can probably afford to get a bit hotter than that-- the
fluid won't boil until perhaps 170C. If the disk is hotter then its
dissipation to the air will be better (bigger temperature gradient).