  Fitting equilibrium dynamical models to observational data is an essential
step in understanding the structure of the gaseous hot haloes that surround our
own and other galaxies. However, the two main categories of models that are
used in the literature are poorly suited for this task: (i) simple barotropic
models are analytic and can therefore be adjusted to match the observations,
but are clearly unrealistic because the rotational velocity $v_\phi(R,z)$ does
not depend on the distance $z$ from the galactic plane, while (ii) models
obtained as a result of cosmological galaxy formation simulations are more
realistic, but are impractical to fit to observations due to high computational
cost. Here we bridge this gap by presenting a general method to construct
axisymmetric baroclinic equilibrium models of rotating galactic coronae in
arbitrary external potentials. We consider in particular a family of models
whose equipressure surfaces in the $(R,z)$ plane are ellipses of varying axis
ratio. These models are defined by two one-dimensional functions, the axial
ratio of pressure $q_{\rm axis}(z)$ and the value of the pressure $P_{\rm
axis}(z)$ along the galaxy's symmetry axis. These models can have a rotation
speed $v_\phi(R,z)$ that realistically decreases as one moves away from the
galactic plane, and can reproduce the angular momentum distribution found in
cosmological simulations. The models are computationally cheap to construct and
can thus be used in fitting algorithms. We provide a python code that given
$q_{\rm axis}(z)$, $P_{\rm axis}(z)$ and $\Phi(R,z)$ returns $\rho(R,z)$,
$T(R,z)$, $P(R,z)$, $v_\phi(R,z)$. We show a few examples of these models using
the Milky Way as a case study.
