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

In all honesty, I got lost in the last reading. But my feeling on how you describe heat seems to me a little simpler. If you imagine that you are in an absolutely cold room. Everything is still and that room is the universe (all there is, everything you see, touch, etc). That means that there is no heat loss outside of that room because if there were, the heat is part of this universe and so this universe is bigger than we thought and must include that heat loss.
If you than add one heat source (I was going to say hot iron balls as this is an analogy I have experienced). No more energy or heat is being added to these heat sources. Now if you think of the communication of that energy, or heat as English would describe it, that heat travels at a certain speed, which is the speed of light. Given a sufficiently large room, non of that heat will be reflected of the walls of the room and head back towards their source. The amount energy generated by the heat source must eventually be decreasing, if we assume laws of thermodynamics.
The equilibrium state must be when the energy is reflected of the walls of the Universe and must occur when the number of heat particles hitting the source equal the number of heat particles leaving the source (assuming the two heat particles do not interact by producing a non heat particle).
So that implies that if the universe is getting cooler than the particles have not found a wall, or have not returned yet from the walls.
The equilibrium is a the point when the number of heat particles leaving is equals to the number of heat particles entering the source regardless of which source you mean. As heat is a commodity, we cannot differentiate it, from particle to particle. In some cases we think that the particle is the same. It may be or it may not be.