I would want to call this question [science-based], except that we need to restrict ourselves to newtonian/"pre-relativity" physics.
(Clarification: for this question, by "rigid body", I mean an object which is completely incapable of flexing/bending, stretching, or being compressed. This is, of course, impossible under special/general relativity--such an object could be used to send information at faster-than-light speeds. But if we're looking at a physics "simulation" based simply on mass, momentum, and perfectly-elastic collisions, I'm hoping that such a concept ought to be treatable...)
Let's assume we have a rigid body. We'll black-box what it's made of (I have thoughts about it, but they would probably add unnecessary complication to the question), but it has all the inertial properties one would expect of solid matter (mass, density, momentum, moment of inertia, etc). Any molecules or atoms that would enter the space contained by the rigid body instead behave as though they had collided with another molecule or atom, and all the imparted momentum that would go with such a collision takes place. What I'm wondering is...if this is all we know about how a rigid body works, do we have enough to make an educated guess about its thermal conductivity?
To help us think about it, let's do an experiment!
I have a rigid body of this sort which is shaped like a really long dumbbell (say, two 1-foot-diameter spheres which are connected to each other by a 100-foot long bar). I've melted two batches of metal, and I dip each end of this rigid body into one of the batches and let it cool and set around it. So now I have two lumps of metal connected by a rigid, 100-foot bar.
I also have a vacuum chamber big enough to house this assembly, an electrical hot plate that's safe to run in a vacuum, a pair of thermometers, and a bunch of mirrors.
- I put the partially metal-encased rigid body in the vacuum chamber. One of the lumps of metal is sitting on the hot plate.
- I sit a thermometer on top of each lump of metal.
- I set up mirrors so that the lumps of metal have almost no line-of-sight on each other; and any black-body radiation they emit is mostly reflected back at them.
- I empty the chamber of air, hoping to minimize heat transfer from conduction and convection.
- I turn on the hotplate under the lump of metal at one end of the rigid body, and I start observing the thermometers.
What are my results, if we can reason about them at all?
Can we expect a rigid body to transfer heat efficiently, essentially via a sort of Brownian motion? Would vibration parallel with the bar transmit more efficiently than vibration perpendicular to the bar, because of the reduced angular motion at the other end?