The 78 secondary eclipse depths for a sample of 36 transiting hot Jupiters observed at 3.6- and 4.5 μm using the Spitzer Space Telescope is here reported. Eclipse results for 27 of these planets are new and include highly irradiated worlds such as KELT-7b (Kilodegree Extremely Little Telescope), WASP-87b (Wide Angle Search for Planets), WASP-76b, and WASP-64b, and important targets for the James Webb Space Telescope (JWST) such as WASP-62b. WASP-62b is found to have a slightly eccentric orbit (ecosω=0.00614±0.00058), and the eccentricities of HAT-P-13b (Hungarian Automated Telescope Project) and WASP-14b are confirmed. The remainder are individually consistent with circular orbits, but there is statistical evidence for eccentricity increasing with orbital period in this range from 1 to 5 days. Day-side brightness temperatures (Tb) for the planets yield information on albedo and heat redistribution, following Cowan and Agol (2011). Planets having maximum day side temperatures exceeding ∼2200 K are consistent with zero albedo and distribution of stellar irradiance uniformly over the day-side hemisphere. The most intriguing result is a detection of 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 98±26 parts-per-million per Kelvin, over the entire temperature range in the sample (800K to 2500K). No existing model predicts this trend over such a large range of temperature. This may be due to a structural difference in the atmospheric temperature profile between the real planetary atmospheres as compared to models.