  We consider a plasma described by means of a two-dimensional fluid model
across a constant but non-uniform magnetic field $\mathbf{B} = B(x,y)
\mathbf{\hat{z}}$. The dynamical evolution of the density and the vorticity
takes into account the interchange instability and magnetic field
inhomogeneities. First, in order to described the Finite Larmor Radius effects
we apply the gyromap to build a Hamiltonian model with ion temperature from a
cold-ion model. Second, we show that the gyromap is justified using
Braginskii's closure for the stress tensor as well as an apt ordering on the
fluctuating quantities.
