We present Spitzer 7.6-14.5 μm spectra of ULAS J003402.77-005206.7 and ULAS J133553.45+113005.2, two T9 dwarfs with the latest spectral types currently known. We fit synthetic spectra and photometry to the near- through mid-infrared energy distributions of these dwarfs and that of the T8 dwarf 2MASS J09393548-2448279. We also analyze near-infrared data for another T9, CFBD J005910.82-011401.3. We find that the ratio of the mid- to near-infrared fluxes is very sensitive to effective temperature at these low temperatures, and that the 2.2 μm and 4.5 μm fluxes are sensitive to metallicity and gravity; increasing gravity has a similar effect to decreasing metallicity, and vice versa, and there is a degeneracy between these parameters. The 4.5 μm and 10 μm fluxes are also sensitive to vertical transport of gas through the atmosphere, which we find to be significant for these dwarfs. The full near- through mid-infrared spectral energy distribution allows us to constrain the effective temperature (K)/gravity (ms-2)/metallicity ([m/H] dex) of ULAS J0034-00 and ULAS J1335+11 to 550-600/100-300/0.0-0.3 and 500-550/100-300/0.0-0.3, respectively. These fits imply low masses and young ages for the dwarfs of 5-20 M Jupiter and 0.1-2 Gyr. The fits to 2MASS J0939-24 are in good agreement with the measured distance, the observational data, and the earlier T8 near-infrared spectral type if it is a slightly metal-poor 4-10 Gyr old system consisting of a 500 K and 700 K, ~25 M Jupiter and ~40 M Jupiter, pair, although it is also possible that it is an identical pair of 600 K, 30 M Jupiter, dwarfs. As no mid-infrared data are available for CFBD J0059-01 its properties are less well constrained; nevertheless it appears to be a 550-600 K dwarf with g= 300-2000 ms-2 and [m/H] = 0-0.3 dex. These properties correspond to mass and age ranges of 10-50 M Jupiter and 0.5-10 Gyr for this dwarf.