This heat absorption works so well that the feathers eventually *exceed* the ambient temperature of the environment and reverse the flow of heat. So now instead of the bird sweltering in this heat, it is instead, rather cool.
The surface temperature of almost any material exposed to radiant heat will rise above ambient air temperature, so the situation you cite is not exceptional at all. In fact, ambient air temperature (or even the absence of air) doesn't have much to do with the radiant transfer of heat. I suspect you mean that the feathers are more effectively blocking the radiant heat from reaching the surface of the skin through increased absorption and that the insulating air layer between the skin and the feathers helps prevent that absorbed heat from conducting to the skin of the animal. The reverse of this is seen in animals like the polar bear, which have thick but essentially transparent hair which allows the radiant heat of the sun to reach and warm the skin while the providing insulating layers of air to slow the rate of conductive heat loss. The flow of heat isn't "reversed" in one case relative to the other, it's merely a different arrangement of absorptive versus insulating layers.