  Half of the energy emitted by late-T- and Y-type brown dwarfs emerges at 3.5
< lambda um < 5.5. We present new L' (3.43 < lambda um < 4.11) photometry
obtained at the Gemini North telescope for nine late-T and Y dwarfs, and
synthesize L' from spectra for an additional two dwarfs. The targets include
two binary systems which were imaged at a resolution of 0.25". One of these,
WISEP J045853.90+643452.6AB, shows significant motion, and we present an
astrometric analysis of the binary using Hubble Space Telescope, Keck Adaptive
Optics, and Gemini images. We compare lambda ~4um observations to models, and
find that the model fluxes are too low for brown dwarfs cooler than ~700K. The
discrepancy increases with decreasing temperature, and is a factor of ~2 at
T_eff=500K and ~4 at T_eff=400K. Warming the upper layers of a model atmosphere
generates a spectrum closer to what is observed. The thermal structure of cool
brown dwarf atmospheres above the radiative-convective boundary may not be
adequately modelled using pure radiative equilibrium; instead heat may be
introduced by thermochemical instabilities (previously suggested for the L- to
T-type transition) or by breaking gravity waves (previously suggested for the
solar system giant planets). One-dimensional models may not capture these
atmospheres, which likely have both horizontal and vertical
pressure/temperature variations.
