How might a resonant antenna and black body radiation interact? How does an antenna behave when it is cooled so that its black-body radiation is emitting energy at its resonant frequency?
Edit: To clarify, its not how they're related in general, but how might thermal radiation and resonance interact with each other when their spectra are aligned well?
Edit: Also, I'm sure that the thermal radiation spectra that have a significant peaks are associated with incredibly high temperatures, and peak at incredibly small wavelengths, rendering such an antenna completely impractical to build. Still, I'm still interested in the theoretical concept.
 A: OK, the simple answer:
When there is  a resonance in the antenna  you have a coherent phenomenon. All the bands of electrons of the antenna are marching in tune. 
The black body radiation is an incoherent phenomenon coming from the individual atoms of the antenna. Even if the peak of the black body radiation were sitting on the resonance of the antenna it is still an incoherent phenomenon that cannot couple to the coherent behavior of the electrons in the current that resonate. 
Think of a single violin tune and a crowd of people talking. The noise of the people does not cover the clarity of the violin even in high volumes.
A: They're not related. The black-body radiation as well as the resonance curve may look like "bumps" but they are very different bumps mathematically. The black body radiation gets emitted at all frequencies, and the "uncertainty of the frequency" is maximized, in some sense. On the other hand, resonances are peaked around a particular frequency.
Resonance curves are about matrix elements between pure states; thermal curves are traces over the whole Hilbert spaces so they arise from mixed stated. That's why the exponentials only appear in the thermal curves.
So the only thing they share is that they produce intensities as a function of frequency - but many other things in physics do the same thing - and in both cases, complex numbers are useful ($E_0-i\Gamma/2$ for resonances and imaginary time $i\beta$ in the thermal case) - but complex numbers are useful across physics.
