  We construct magnetostatic models of coronal loops in which the
thermodynamics of the loop is fully consistent with the shape and geometry of
the loop. This is achieved by treating the loop as a thin, compact, magnetic
fibril that is a small departure from a force-free state. The density along the
loop is related to the loop's curvature by requiring that the Lorentz force
arising from this deviation is balanced by buoyancy. This equilibrium, coupled
with hydrostatic balance and the ideal gas law, then connects the temperature
of the loop with the curvature of the loop without resorting to a detailed
treatment of heating and cooling. We present two example solutions: one with a
spatially invariant magnetic Bond number (the dimensionless ratio of buoyancy
to Lorentz forces) and the other with a constant radius of curvature of the
loop's axis. We find that the density and temperature profiles are quite
sensitive to curvature variations along the loop, even for loops with similar
aspect ratios.
