We report 78 secondary eclipse depths for a sample of 36 transiting hot Jupiters observed at 3.6- and 4.5 microns using the Spitzer Space Telescope. Our eclipse results for 27 of these planets are new, and include highly irradiated worlds such as KELT-7b, WASP-87b, WASP-76b, and WASP-64b, and important targets for JWST such as WASP-62b. We find that WASP-62b has a slightly eccentric orbit e cos(omega) = 0.00614+/- 0.00064, and we confirm the eccentricity of HAT-P-13b and WASP-14b. The remainder are individually consistent with circular orbits, but we find statistical evidence for eccentricity increasing with orbital period in our range from 1 to 5 days. Our day-side brightness temperatures for the planets yield information on albedo and heat redistribution, following Cowan and Agol (2011). Planets having maximum day side temperatures exceeding ~ 2200K are consistent with zero albedo and distribution of stellar irradiance uniformly over the day-side hemisphere. Our most intriguing result is that we detect a systematic difference between the emergent spectra of these hot Jupiters as compared to blackbodies. The ratio of observed brightness temperatures, Tb(4.5)/Tb(3.6), increases with equilibrium temperature by 100 +/- 24 parts-per-million per Kelvin, over the entire temperature range in our sample (800K to 2500K). No existing model predicts this trend over such a large range of temperature. We suggest that this may be due to a structural difference in the atmospheric temperature profile between the real planetary atmospheres as compared to models.
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