  Coronal holes and active regions are typical magnetic structures found in the
solar atmosphere. We propose several magnetohydrostatic equilibrium solutions
that are representative of these structures in two dimensions. Our models
include the effect of a finite plasma-$\beta$ and gravity, but the distinctive
feature is that we incorporate a thermal structure with properties similar to
those reported by observations. We developed a semi-analytical method to
compute the equilibrium configuration. Using this method, we obtain cold and
under-dense plasma structures in open magnetic fields representing coronal
holes, while in closed magnetic configurations, we achieve the characteristic
hot and over-dense plasma arrangements of active regions. Although coronal
holes and active regions seem to be antagonistic structures, we find that they
can be described using a common thermal structure that depends on the flux
function. In addition to the force balance, the energy balance is included in
the constructed models using an a posteriori approach. From the two-dimensional
computation of thermal conduction and radiative losses in our models, we infer
the required heating function to achieve energy equilibrium. We find that the
temperature dependence on height is an important parameter that may prevent the
system from accomplishing thermal balance at certain spatial locations. The
implications of these results are discussed in detail.
