  This paper mainly considers three iterations based on charge-conservative
finite element approximation in Lipschitz domain for the stationary thermally
coupled inductionless MHD equations. Based on the hybrid finite element method,
the unknowns of hydrodynamic are discretized by the stable velocity-pressure
finite element pair, and the current density along with electric potential are
similarly discretized by the comforming finite element pair in
$\boldsymbol{H}(\boldsymbol{div}, \Omega)\times L^2(\Omega)$. And on account of
the strong nonlinearity of the equations, we present three coupled iterative
methods, namely, the Stokes, Newton and Oseen iteration and the convergence and
stability under different uniqueness conditions are analyzed strictly. It is
proved especially that the error estimates of velocity, current density,
temperature and pressure do not depend on potential. The theoretical analysis
is validated by the given numerical results, and for the proposed methods, the
applicability and effectiveness are demonstrated.
