2nd Law or 2-way Radiative Heat Transfer?

In the present discussion of the 2nd Law of Thermodynamics let us go back to this post from 2011 exposing the 19th century battle between 1-way transfer (Pictet) vs 2-way transfer (Prevost) of heat energy by radiation playing a central role in climate science today. 

In 1-way transfer a warm body heats a colder body in accordance with the 2nd Law. 

In 2-way heat transfer both warm and cold bodies are viewed to heat each other, but the warm heats more and so there is a net transfer of heat energy from warm to cold. But a cold body heating a warm body violates the 2nd Law of thermodynamics, and so there is something fishy here. 

Yet the basic mathematical model of radiative heat transfer in the form of Schwarzschild's equation involve 2-way transfer of heat energy, in apparent violation of the 2nd Law. 

I have discussed this situation at length on this blog with tags such as 2nd law of thermodynamics and radiative heat transfer with more on Computational Blackbody Radiation.

If you worry about the 2nd Law, you can ask yourself how 2-way radiative heat transfer is physically possible, when it appears to violate the 2nd Law? What is false here: 2nd Law or 2-way heat transfer?

What is your verdict?