  Because WISE J085510.83$-$071442.5 (hereafter WISE 0855-0714) is the coldest
known brown dwarf ($\sim250$ K) and one of the Sun's closest neighbors (2.2
pc), it offers a unique opportunity for studying a planet-like atmosphere in an
unexplored regime of temperature. To detect and characterize inhomogeneities in
its atmosphere (e.g., patchy clouds, hot spots), we have performed time-series
photometric monitoring of WISE 0855-0714 at 3.6 and 4.5 micron with the Spitzer
Space Telescope during two 23~hr periods that were separated by several months.
For both bands, we have detected variability with peak-to-peak amplitudes of
4-5% and 3-4% in the first and second epochs, respectively. The light curves
are semi-periodic in the first epoch for both bands, but are more irregular in
the second epoch. Models of patchy clouds have predicted a large increase in
mid-IR variability amplitudes (for a given cloud covering fraction) with the
appearance of water ice clouds at $T_{\rm eff}<$375 K, so if such clouds are
responsible for the variability of WISE 0855-0714, then its small amplitudes of
variability indicate a very small deviation in cloud coverage between
hemispheres. Alternatively, the similarity in mid-IR variability amplitudes
between WISE 0855-0714 and somewhat warmer T and Y dwarfs may suggest that they
share a common origin for their variability (i.e., not water clouds). In
addition to our variability data, we have examined other constraints on the
presence of water ice clouds in the atmosphere of WISE 0855-0714, including the
recent mid-IR spectrum from \citet{ske16}. We find that robust evidence of such
clouds is not yet available.
