Isn't this something we already know from the mass–energy equivalence? In the same way that a nuclear reaction that produces heat must cost the object mass (and therefore gravitational pull)
It does, but because you have to divide the energy change by c^2, it is really really hard to detect it, and mostly overwhelmed by other effects of the heating/cooling.
why do the units matter here? Under this theory, will a body at absolute zero have no observable mass? No attractive field around it, no inertia if you try to move it.
Isn't this something we already know from the mass–energy equivalence? In the same way that a nuclear reaction that produces heat must cost the object mass (and therefore gravitational pull)