I've thought about , I've searched the web , I've taught myself StefanBoltzmann and Kirchoff  and still I don't understand how uniformly changing the color of a radiantly heated ball in a vacuum can change its mean temperature . It violates basic notions I learned reading boy's science books as a kid in the '50s . The idea that making an essentially minute change in the spectrum of the atmosphere by changing its composition by one part in ten thousand seemed so unreasonable to me that I conducted a "Mr Wizard" experiment last spring to see what the difference would be between black and white balls .
The 0th law of thermodynamics says that things asymptote to the same temperature with each other . The The StefanBoltzmann law relates the temperature of an object in equilibrium to the fourth root of the radiant energy density of its surroundings . Simple calculations show that seems to predict the mean temperature of the inner planets except Venus to within observational error . Venus is about two and a quarter times the expected temperature of a black body in its orbit . Yet the claim is made that its atmospheric stack of CO2 filtering the sun's energy "traps" that heat . Can we not , then , construct a perpetual heat engine ?
The Wikipedia page on the StefanBoltzmann law had a less ambitious explanation of a gap in temperature requiring a "greenhouse" effect to explain . It claimed that the "effective" temperature of a radiated sphere is reduced by the 4th root of its absorptivity ( 1  its reflectance ) , or about 30 kelvin in the case of the earth . I pointed on the discussion page that such a law leads to the possibility that you could coat the inner chamber of a vacuum bottle with magnesium oxide with a reflectivity of about 0.9 and it should come to an equilibrium temperature of about minus 100 Celsius . This led to some changes in the Wikipedia page , but not enough .
The bottom line is , on the publicly available internet , I have been unable to find either the quantitative physical equations for the "greenhouse" effect or any experimental confirmation and parameterization of it . Being independent , I am seeking partners with access to the resources , eg , a vacuum chamber , etc , to experimentally and theoretically study the temperature physics of radiantly heated colored spheres . I can be contacted thru www.CoSy.com which contains my work up to the present .
