"You contend that spacetime is 'physically real, yet all it is, is measures of duration and distance."
So you think. Physically real means " ... independent in its properties, having a physical effect yet not itself influenced by physical conditions." The measure of temperature is influenced by physical conditions, and so not physically real.
"Which are relative to physical effects, like acceleration, velocity and gravity. Not to mention using completely arbitrary points of reference in the first place!"
So you think. Physically real spacetime interacts with mass points; these are relative, not arbitrary, even though they can be arbitrarily chosen.
"If you were to take an ideal gas and compress its volume, the temperature would rise in proportion. Why don't we say temperature is the fourth dimension of volume?"
Because you don't have a clue to how adding energy to the system by compressing it is symmetric to the energy increase in the gas.
"And as I keep pointing out, these molecules are also running into each other and transferring their energy to each other, creating that thermal medium."
No, John, the work of compression creates that thermal medium. Now matter how many times you keep pointing out your error.
"Now if there was none of this thermal interaction and it really was just an average of the motion of distinct molecules, you would have more of an argument."
I would, eh? It's simple thermodynamics, not magic.
Best,
Tom