Only kinetic energy does not contribute to mass. In fact, it's even narrower: only the kinetic energy of the center of mass does not contribute. For example, he

Only kinetic energy does not contribute to mass. In fact, it's even narrower: only the kinetic energy of the center of mass does not contribute. For example, heat energy is really just kinetic energy of the constituent particles, and heat definitely contributes to mass. The essential idea is that mass is Lorentz invariant, which means it does not change under changes of coordinate systems. So mass must be independent of velocity and orientation, which are just artifacts of how you measure anyways.