At the end of the (fourth), 1905’s E=mc² paper Einstein claimed: “The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference”. This sounds odd to me, given that the change L(γ-1) in kinetic energy resulted from calculating radiation energy. Light emitted in the two opposite directions has the same speed for any reference system, and that is a special property which holds for light only. If you think of the symmetric heat release without a change in the rest state of the body in the rest reference system, then no change in velocity should be observed from the moving inertial system too. But the same would not be true respect to the particles in thermal motion. A different Doppler effect (corresponding to different temperatures and thermal propagation rate) should be calculated from the moving system for the total amount of thermal energy emission from the two sides (as resulted for the light). But I would expect a kinetic energy change different from L(γ-1). Would somebody like to help me understand the basis of Einstein’s implicit deduction?