We present observational evidence for the inhibition of bar formation in dispersion-dominated (dynamically hot) galaxies by studying the relationship between galactic structure and host galaxy kinematics in a sample of 257 galaxies between 0.1 < z ≤ 0.84 from the All-Wavelength Extended Groth Strip International Survey and the Deep Extragalactic Evolutionary Probe 2 survey. We find that bars are preferentially found in galaxies that are massive and dynamically cold (rotation-dominated) and on the stellar Tully-Fisher relationship, as is the case for barred spirals in the local universe. The data provide at least one explanation for the steep (×3) decline in the overall bar fraction from z = 0 to z = 0.84 in L* and brighter disks seen in previous studies. The decline in the bar fraction at high redshift is almost exclusively in the lower mass (10 < log M *(M ⊙) < 11), later-type, and bluer galaxies. A proposed explanation for this "downsizing" of the bar formation/stellar structure formation is that the lower mass galaxies may not form bars because they could be dynamically hotter than more massive systems from the increased turbulence of accreting gas, elevated star formation, and/or increased interaction/merger rate at higher redshifts. The evidence presented here provides observational support for this hypothesis. However, the data also show that not every disk galaxy that is massive and cold has a stellar bar, suggesting that mass and dynamic coldness of a disk are necessary but not sufficient conditions for bar formation - a secondary process, perhaps the interaction history between the dark matter halo and the baryonic matter, may play an important role in bar formation. © 2012. The American Astronomical Society. All rights reserved.