<p>The boundary value and the multiplicative control problems for stationary equations of magnetohydrodynamics of viscous heat-conducting fluid are studied. For the magnetic field we use an impedance boundary condition, for the temperature mixed boundary conditions are chosen; and for the velocity a homogeneous Dirichlet condition is used. It is assumed that the coefficients of impedance and of thermal exchange in the boundary conditions and thermal expansion coefficient in the impulse equation depend nonlinearly on temperature and also depend on spatial variables. The global solvability of the boundary value and extremum problems is proved, sufficient conditions for the local uniqueness of the solution of the boundary value problem are established. For the extremum problem an optimality system is derived. With the help of this system the bang–bang principle for some multiplicative controls is established.</p>