From my high school physics classes:
The effect of a surface consistency is the same for absorbing ardiation as for emitting radiation. In other words, a black surface is good in absorbing radiation energy (this is why tarmac gets hot in the sun) and also in losing that heat (energy) by emitting radiation. This is why tarmac cools markedly when the sun goes down.
The heat build-up in the skin of the Blackbird is purely due to friction, not radiation. So if you want to get rid of as much of this heat (energy) as possible, which you do, then choose the most efficient way of emitting radiation possible, i.e. paint the thing black.