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Half of the energy emitted by late-T- and Y-type brown dwarfs emerges at 3.5 ≤ λμm ≤ 5.5. We present new L′ (3.43 ≤ λμm ≤ 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 that 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 λ ∼ 4 μm observations to models, and find that the model fluxes are too low for brown dwarfs cooler than ∼700 K. The discrepancy increases with decreasing temperature, and is a factor of ∼2 at Teff = 500 K and ∼4 at Teff = 400 K. 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 modeled 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. [ABSTRACT FROM AUTHOR]