Are good absorbers of heat also good radiators?
Suppose you had two objects, similar except that one is a good radiator of heat and a poor absorber, and the other is a good absorber of heat and a poor radiator. Have them at the same temperature and set them next to each other (in a vacuum (in a container with perfectly reflective walls so that no heat is lost -not necessary but makes it more dramatic)). At a given temperature the good radiator will radiate more energy than the poor radiator, and being a poor absorber it will absorb less. Thus energy will be transferred from the good radiator to the poor, causing the former to cool down while the latter heats up until the difference in temperature compensates for their different absorptive/radiative properties. Concentrating the heat into one body like this constitutes a decrease in entropy for the system, which cannot happen. And if it did, you could hook up a heat engine between the warm and cold bodies and obtain work from the flow of heat from the warm to cold. This would tend to decrease the temperature difference, allowing the radiative difference to continue to maintain the temperature difference. You would have a perpetual motion machine.
More generally, if some object were a good absorber and poor radiator (compared to average objects), it would tend to maintain a temperature above ambient. You could leave a bunch of objects in a closed box overnight. When you open the box and measure the temperature of each object, they would all be different, their temperature depending on whether they are good absorbers or good radiators.