Lets try this again

[J.C.MacSwell]

The fundamental particles for which rest mass is usually used cannot be "heated up" as such' date=' since temperature implies an ensemble of atoms in thermal equilibrium, not an individual particle.

 

I don't think the mass of such an ensemble [b']could[/b] be considered the rest mass, since it is true that the mass would depend on the total energy it has in its rest frame. Imagine you took a snapshot of the system, so you measured all pertinent values at some time: the constituent particle would each have some KE, which would have to transform into some other reference frame, and while total energy is conserved, the value of that energy does not remain the same in different frames. I don't know off the top of my head how the average energy would end up - observers in two frames might not agree on the mass of the system. So it's not an invariant mass; the constituent particles are all in different reference frames. I don't know how much of thermodynamics has been treated relativistically.

 

In the rest frame of the body I think it could be considered its "effective rest mass" or ERM (I am making up a term). I think this ERM would be invariant with changes of reference frame similar to the way a rest mass of a particle is invariant. The particles are in different rest frames and the sum of their invariant masses are less (normally insignificantly) than the ERM of the body they make up but the sum of their relativistic masses are always greater (again normally insignificantly and by the same amout) than the "effective relativistic mass" or ERLVM (another term) of the body. So it all adds up consistently even if different in each frame.

 

To me this "seems" like mass, whatever it is. (and whatever mass is)