  We present new L' (3.75 um) photometry of six L and T dwarfs, and M' (4.70
um) photometry of ten L and T dwarfs, observed at Gemini Observatory, and new
3.55, 4.49, 5.73 and 7.87 um photometry of nine L and T dwarfs, obtained with
the Spitzer Space Telescope. The sample includes unusually blue and red dwarfs
from our near-infrared studies. The data are combined with published L', M' and
Spitzer photometry of L and T dwarfs, and trends of colors with spectral type
and other colors are examined. Model atmospheres by Marley and Saumon are used
to generate synthetic colors for ranges of effective temperature, gravity,
grain sedimentation efficiency, metallicity and vertical mixing efficiency. We
explore how these parameters affect the mid-infrared colors of L and T dwarfs
and find that the data are modelled satisfactorily only if substantial vertical
mixing occurs in both L- and T-dwarf atmospheres. The location and range of the
L and T dwarf sequences in IRAC color-color and color - magnitude diagrams is
also only reproduced if this mixing occurs, with a range of efficiency
described by K_zz ~ 10^2-10^6 cm^2/s. The colors of the unusually red dwarfs
are best reproduced by non-equilibrium models with low sedimentation
efficiency, i.e. thick cloud decks, and those of the unusually blue dwarfs by
non-equilibrium models with high sedimentation efficiency, i.e. thin cloud
decks. The K-L' and Spitzer [3.55]-[4.49] colors can be used as indicators of
effective temperature for L and T dwarfs, but care must be taken to include
gravity and metallicity effects for late-T dwarfs and vertical mixing for both
late-L and T dwarfs.
