Assume an adiabatic room and some objects in it. Heat is only able to exchange via radiation.
All of the objects and the internal walls have arbitrary $\alpha$'s.
After a long time, take a "shot" of the system.
Is it possible for some values of $\alpha$ for each object and some initial conditions to be arranged in a way that we have, in the long-term stationary, different stable temperatures of different objects?
This will help me get a sense of the exact definition of thermal equilibrium and its relation with stationary temperature state for an object.
An intuitive proof would be better, if any.