And again, you demonstrate that you simply don't understand....Slowed cooling is not warming...the people in the room are not gaining any energy at all from the cooler walls.
Look at the equation.....
See the P...that is the net radiated power....The magnitude of that number is entirely dependent upon the difference between the radiator and its surroundings....the f'ing equation answers your question regarding different heat loss at different temperatures.
Again...look at the equation
. P is net radiated power of the radiator...A is the radiating area....sigma is Stefan's constant....e is the emissivity.....T is the temperature of the radiator....and Tc is the temperature of the surroundings....increase the temperature difference between the radiator and its surroundings and you increase P....decrease the difference between the radiator and its surroundings and you decrease P. The people in the room aren't getting energy from the walls...they are still losing energy...they are simply radiating less because the difference between their own temperature and the walls has decreased and thus P has decreased....there is no back radiation...they aren't gaining even the slightest trace of energy from the walls.
This equation

describes a one way gross flow of energy
This is what the equation must look ike if you want to show a two way net flow of energy...

Interestingly enough, this version of the SB equation is used by climate science, but not hard physics...Hard science grasps that the SB law is stated in a particular manner because it describes a particular thing...that is, one way, gross energy flow....the soft science of climate science has no hesitation at altering a stated physical law to make it show what they wish it to show whether it is true or not.
There is no such thing as back radiation....energy won't move from a cooler object to a warmer object without some work having been done to accomplish the task.