  Filamentary structures are recognized as a fundamental component of
interstellar molecular clouds in observations by the Herschel satellite. These
filaments, especially massive filaments, often extend in a direction
perpendicular to the interstellar magnetic field. Furthermore, the filaments
sometimes have an apparently negative temperature gradient, that is, their
temperature decreases towards the center. In this paper, we study the
magnetohydrostatic equilibrium state of negative-indexed polytropic gas with
the magnetic field running perpendicular to the axis of the filament. The model
is controlled by four parameters: center-to-surface density ratio
($\rho_c/\rho_s$), plasma $\beta$ of the surrounding gas, radius of the parent
cloud $R'_0$ normalized by the scale height, and the polytropic index $N$. The
steepness of the temperature gradient is represented by $N$. We found that the
envelope of the column density profile becomes shallow when the temperature
gradient is large. This reconciles the inconsistency between the observed
profiles and those expected from the isothermal models. We compared the maximum
line-mass (mass per unit length), above which there is no equilibrium, with
that of the isothermal non-magnetized filament. We obtained an empirical
formula to express the maximum line-mass of a magnetized polytropic filament as
$\lambda_{max}\simeq\left[{\left(\lambda_{0,max}(N)/M_\odot{\rm
pc^{-1}}\right)^2+\left(5.0+6.0/N\right)\left({\Phi_{cl}}/{1\mu {\rm
G\,pc}}\right)^2}\right]^{1/2}M_\odot {\rm pc^{-1}}$, where
$\lambda_{0,max}(N)$ represents the maximum line-mass of the non-magnetized
filament and $\Phi_{cl}$ indicates one-half of the magnetic flux threading the
filament per unit length. Although the negative-indexed polytrope makes the
maximum line-mass decrease compared with that of the isothermal model, a
magnetic field threading the filament increases the line-mass.
