  There are no field brown dwarf analogs with measured masses, radii, and
luminosities, precluding our ability to connect the population of transiting
brown dwarfs with measurable masses and radii and field brown dwarfs with
measurable luminosities and atmospheric properties. LHS 6343 C, a
weakly-irradiated brown dwarf transiting one member of an M+M binary in the
Kepler field, provides the first opportunity to probe the atmosphere of a
non-inflated brown dwarf with a measured mass and radius. Here, we analyze four
Spitzer observations of secondary eclipses of LHS 6343 C behind LHS 6343 A.
Jointly fitting the eclipses with a Gaussian process noise model of the
instrumental systematics, we measure eclipse depths of 1.06 \pm 0.21 ppt at 3.6
microns and 2.09 \pm 0.08 ppt at 4.5 microns, corresponding to brightness
temperatures of 1026 \pm 57 K and 1249 \pm 36 K, respectively. We then apply
brown dwarf evolutionary models to infer a bolometric luminosity log(L_star /
L_sun) = -5.16 \pm 0.04. Given the known physical properties of the brown dwarf
and the two M dwarfs in the LHS 6343 C system, these depths are consistent with
models of a 1100 K T dwarf at an age of 5 Gyr and empirical observations of
field T5-6 dwarfs with temperatures of 1070 \pm 130 K. We investigate the
possibility that the orbit of LHS 6343 C has been altered by the Kozai-Lidov
mechanism and propose additional astrometric or Rossiter-McLaughlin
measurements of the system to probe the dynamical history of the system.
