The law of thermal equilibrium is a nice example of how in nature everything is ultimately fairly distributed. Nothing is allowed to keep heat energy for itself without limit. Everything stands in relationship to everything else, and heat is constantly being exchanged in an endless striving to achieve a uniform temperature everywhere.
Liquids and gases exchange heat chiefly by means of convection. With solids this happens by means of radiation and - when there is contact - by means of conduction. And this continues until both objects have the same temperature.
Whether "cold radiation" exists is a question of definition. Cold radiation is the absence of warm radiation, because photons are always "loaded" with heat, even though they are sometimes few in number. When we feel a cold radiation, this is because the object which is sending out this radiation is producing less radiant heat than we are ourselves. When we are in a room with cold walls, we feel a cold radiation that means nothing else than that the law of thermal equilibrium is operating to our disadvantage. When we put on more clothes, we are not in the least preventing less "cold radiation" by the walls from reaching us, because we are thus shielding off the little bit of heat radiation that we otherwise could receive from them. It does mean, however, that we ourselves are losing less radiant heat, and that is the deciding factor.
In the same way, a TULIKIVI soapstone stove is also continually exchanging heat with its environment. If the walls around it, for example, are poorly insulated, then not only will they cool off faster, but the soapstone stove will do so as well.