In modern physics there exist several formulations of relativistic thermodynamics of a moving body. The Planck and Ott formalisms are the main ones. However, it is not clear which one is correct. In the present study, we have solved this problem. We have required the equivalence of the dynamical Hamiltonian of a system to the fundamental thermodynamic potential in addition to the principle of entropy invariance and derived the first law of thermodynamics from this fundamental potential. We have found that in the case of momentum being an independent variable in the Hamiltonian, the Lorentz transformations of the thermodynamic quantities belong to the Planck formalism. However, if we suppose that the velocity is an independent variable in the Hamiltonian (though it is not correct from the point of view of the relativistic dynamics), the Lorentz transformations of the thermodynamic quantities belong to the Ott formalism. It demonstrates that the Ott formalism cannot be appropriate. Moreover, we have proved that in the Planck description the first law of thermodynamics is covariant and the Legendre transform of the Lagrangian is preserved. However, in the Ott description the first law of thermodynamics is not covariant and the Legendre transform is violated. Thus we have demonstrated that only the Planck formulation of relativistic thermodynamics of a moving body is properly defined and the Ott formalism should be discarded.