S&B is not applicable in this thought exercise.
That's nice. It doesn't matter. Your claim still fails energy conservation, whether S&B applies or not. I only brought it up to give a rough idea of the temperature increase of the lamp.
Neither of the two objects are blackbodies and neither of them are in equilibrium with their environment. They are in equilibrium with one another, not the environment...
That's meaningless handwaving. Your claim still violates energy conservation.
The heat coming back through the housing now? LOL, really? what google search gave you that conclusion?
Unlike ivory tower theorists such as you, I don't need google. I just look at the actual world. I reach over, touch my desk lamp, and feel that the lamp housing is hot, and is radiating heat.
Do you, perhaps, have a some kind of magic incandescent lamp that doesn't emit heat through the lamp housing? If so, you might want to bring such a miraculous invention to market.
So your contention is that the energy from each light flows against their opposing yet equal counterpart and effects real heat change in the apparatus it's connected to?
Restate that in English please? I have no idea what you're saying there.
Let's break it down.
Assume we have two 200-watt heat lamps.
Assume 90% of the energy (180 watts) goes out as radiation through the lens (the "beam"), and 10% (20 watts) is waste heat, heating up the lamp housing to 150F. So at equilibrium, the housings radiate at a steady 20 watts each.
With lamps pointed away from each other, total energy flow out of the entire system into the universe is 400 watts at equilibrium. 360 watts in the 2 beams, and 40 watts in radiation from the lamp housings.
Now aim the lamps at each other. Assume 50% of the beam is absorbed by the other lamp, and 50% is reflected/scattered.
So, now we have the 40 watts from the lamp housing, and 180 watts from the scattered beams going out into the universe. 220 watts total.
Yet the system is producing 400 watts. That extra 180 watts has to go somewhere. So it goes into heating up the lamp housings. The lamp housings will heat up until it they radiate 110 watts each instead of 20 watts. At that point, the new equilibrium is reached.