At the end of Mike Blanton's brown-bag talk at NYU yesterday, Matt Kleban asked: Why don't stars produce emission lines; why only absorption lines? Maryam Modjaz said "because they are hotter on the inside and cooler on the outside". That's true! But it is slightly non-trivial to see why the consequence is always absorption-lines only. And does it mean that if the stars were cold, condensed objects bathed in a hotter radiation field, they would produce emission lines? (I think the answer here might be "yes"; think of a gas cloud bombarded with ionizing radiation.) Also Kleban pointed out that actually the very outside of the Sun is in fact hotter than the surface, which is true, but it must be that this is just so optically thin it barely matters.
In some ways, the biggest paradox about stars is that they aren't all the same temperature: After all, the "surface temperature" of a star is the temperature around the place where the photosphere becomes optically thin; shouldn't this be around 10,000 K for all stars? After all, that's the temperature around which hydrogen atoms recombine (see, for example, the CMB). I don't know any simple answer to this paradoxical question; to my (outsider) perspective it seems like the answer is always all about detailed atomic physics.