  In this work, we develop recent research on the fully mixed virtual element
method (mixed-VEM) based on the Banach space for the stationary Boussinesq
equation to suggest and analyze a new mixed-VEM for the stationary
two-dimensional Boussinesq equation with temperature-dependent parameters in
terms of the pseudostress, vorticity, velocity, pseudoheat vector and
temperature fields. The well-posedness of the continuous formulation is
analyzed utilizing a fixed-point strategy, a smallness assumption on the data,
and some additional regularities on the solution. The discretization for the
mentioned variables is based on the coupling $\mathbb{H}(\mathbf{div}_{6/5})$
-- and $\mathbf{H}(\mathrm{div}_{6/5})$ -- conforming virtual element
techniques. The proposed scheme is rewritten as an equivalent fixed point
operator equation, so that its existence and stability estimates have been
proven. In addition, an a priori convergence analysis is established by
utilizing the C\'ea estimate and a suitable assumption on data for all
variables in their natural norms showing an optimal rate of convergence.
Finally, several numerical examples are presented to illustrate the performance
of the proposed method.
