A very simple model (neglecting many effects, but should still work) is as follows: solar radiation comes in. Some is reflected off clouds, while some passes through the atmosphere. Some reflects immediately back from the Earth, and passes back through the atmosphere.
Incident radiation flux = emissivity sigma T^4 (Stefan-Boltzmann). If emissivity (effectly, absorptivity) doesn't change, neither does T.
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My impression was emissivity does change w/ changed atmosphere, as if we change the BB material w/o changing energy incidence. W/ emissivity decreased, we have the higher temp. Whereas incident radiation doesn't change (as much). Maybe I'm not groking what you're pointing at
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