I'm specifically looking at the case of the Sun's corona emitting light that then heats up other bodies on Earth. These bodies can never attain a higher temperature than the Sun's corona.
I know the obvious answer as to why this is is that the second law of thermodynamics says so. But the fact that the light emitted somehow encodes within it the temperature of the thing that emits it is what is strange to me. Are there not bodies of different temperatures that emit the same frequencies of light? Is there some deeper set of statistical mechanics taking place such that the second law of thermodynamics holds?
It makes sense for bodies directly interacting to end up at the same temperature, and at the microscopic scale this would seem to happen because of electrostatic interactions between the bodies. Whichever atom in an atom-atom interaction has a greater kinetic energy will impart kinetic energy on the atom with a lower kinetic energy until equilibrium. A bit of handwaving, I'm sure, because we are considering classical atom-atom interactions, but it makes quite good sense and probably isn't completely off. However, light seems to somehow encode the temperature of what emitted it, and I can't explain how the second law of thermodynamics holds with it.
Why is it that the light emitted by a body of a certain temperature will not heat up a body of the same or greater temperature? Answers I'd like would sort of explain the interactions taking place such that the second law makes some sort of sense, perhaps with Newton's laws, statistical mechanics, Maxwell's equations... whatever else makes sense would be appreciated, really.