I believe some early ICBMs and Soviet testing used radiative heat shields, but I believe all manned missions from Gagarin on used ablative heat shields. Part of the heat shield melts and that is where a lot of the heat goes. Much more than goes to radiative heat transfer.
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They're saying that the vast majority of the heat energy gets dissipated to the atmosphere. Since heat radiating energy takes TIME, and ends up being very SLOW, the melting material leaving the heat shield would make more sense, since it happens quickly. The effect would be a bright streaking light in the sky trailed by a cloud like exhaust, which is exactly what we see when re-entry occurs, similar to a meteor's action in the sky.
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The Space Shuttle lost a measurable thickness off its tiles each time it re-entered.