Of course you did...if you knew the first thing about the SB law, you would have phrased the question differently...the SB law assumes that T is always warmer than Tc...(the c is for cold)
You and your lackey here are the only humans that I've ever seen who claim such a crazy thing. Here's how the normal people say it works.
Net energy out = A*e*sigma *T1^4 - A*e*sigma T2^4.
The first term is heat radiated out, the second is heat absorbed from the environment. It holds for all combinations of T1 (object temp) and T2 (enviro temp).
Now, since you won't explain your theory in detail, I'm going to take my best attempt at it, based on what you've told us.
If T1 < T2, you say the equation is the same.
If T1 > T2, you say this is the new equation:
Net energy out = A*e*sigma (T1^4 - T2^4) - 0
Where again the first term is energy out, and the second term (the zero) is energy in. It reduces to the same thing as the first equation, but the physical working of the terms is quite different. In your magical system, as soon as the environment temp drops below the object temp, the radiation of the object changes from
A*e*sigma *T1^4
to
A*e*sigma (T1^4 - T2^4)
That is, not only does the environment somehow know not to radiated towards the object, but the object itself makes a very abrupt jump in the way it radiates to the environment, instantly going from radiating strongly to hardly radiating at all.
So, what physical process causes the matter in both the object and in the environment to make such an abrupt change in how they radiate?
Can you think of an experiment to prove your theory is correct? Can you think of an experiment that would disprove it?
Occam's razor says the simplest theory that explains the observed data is most likely to be correct. While you've twisted reality around so that your theory sort of explains the observed data, you version is a far more complicated theory than the mainstream theory. Do you advocate ignoring the razor only in this case?