Objects can't know the temperature of their surroundings in the absence of information (photons) from the surroundings impacting the object.
But you'll never square that circle you've placed yourself in.
So why do you suppose the S-B equation for matter not alone in a vacuum specifies T1-T2? You think it is there just for fun?
So why do you suppose the S-B equation for matter not alone in a vacuum specifies T1-T2?
Because objects emitting toward each other lose/gain energy according to the T1-T2 formula.
Any observed, measured evidence to support that claim? Of course not. But your faith is strong.
Any observed, measured evidence to support that claim?
Yes.
Any observed, measured evidence to support your claim that at equilibrium matter stops emitting?
Of course not. But your delusion is strong.
The 2 of you are still stuck in this groove? Let me try to mitigate this one more time.
I guess both of you agree that an insulated body looses less heat per time.
I also guess that both of you agree that the additional energy to increase the temperature is coming from the sun and not from the layer which insulates the earth.
Or is it already at that stage where the 2 of you diverge ?
If not then consider that the barrier which lessens heat loss also acts as a barrier to transmit heat not just from the inside of the system to the outside but also from the outside to the inside (from the sun to the earth surface). This is quite evident:
How much heat radiation from the sun is absorbed by the thermosphere which is at altitudes > 110 km hotter than the surface. It does not get that hot because it`s heated from the colder layers below it !
The other thing is that if you use the StB equation for this layer to calculate the radiated energy and then convert that back to temperature you would be way out of whack with reality:
the highly diluted gas in this layer can reach 2,500 °C (4,530 °F) during the day.
A normal thermometer might indicate significantly below 0 °C (32 °F), at least at night, because the energy lost by thermal radiation would exceed the energy acquired from the atmospheric gas by direct contact.
Ref.:
Thermosphere - Wikipedia