h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Let me say first that I like your article. It gives a good insight in the seemingly strange world of blackbody radiation.
I just have some problems with the contraption you use to demonstrate a perfect absorber or radiator.
You say it is in thermal equilibrium with its surroundings. This means that it can also exchange energy by convection or conduction through the surrounding air.
Let me suggest another setup.
We start with your container, and hang it from a thermally non-conducting thread inside a larger closed container that is completely absorbing on the inside. To make it more interesting, we cool the whole setup to a constant temperature near zero Kelvin, and evacuate the inside. We now plug the little hole in your container.
Now for real experiments. In order to get the inner container to absorb energy, we light it with a laserbeam. Monochromatic light is theoretically better, but not necessary. The light is (partly) absorbed by the inner container and it will rise in temperature, whilst emitting light depending on the outside color.
In the inside of the small container there will be a perfect black-body radiation belonging to the temperature of the container.
Now we make the little hole again. If there is no laserlight falling into it, it is a perfect emitter of blackbody radiation. If it picks up all the laserlight, it is a perfect absorber, and the temperature of the container will rise some more until a new equilibrium is reached.

Question: If the little hole is made, and the blackbody radiation 'excapes' into the larger space with a lower temperature radiation, will the temperature of the inside container decrease a bit?