The corona is an integral component of active galactic nuclei (AGNs) which produces the bulk of the X-ray emission above 1-2keV. However, many of its physical properties and the mechanisms powering this emission remain a mystery. In particular, the temperature of the coronal plasma has been difficult to constrain for large samples of AGNs, as constraints require high-quality broadband X-ray spectral coverage extending above 10keV in order to measure the high-energy cutoff, which provides constraints on the combination of coronal optical depth and temperature. We present constraints on the coronal temperature for a large sample of Seyfert 1 AGNs selected from the Swift/BAT survey using high-quality hard X-ray data from the NuSTAR observatory combined with simultaneous soft X-ray data from Swift/XRT or XMM-Newton. When applying a physically motivated, nonrelativistic disk-reflection model to the X-ray spectra, we find a mean coronal temperature kT_e_=84+/-9keV. We find no significant correlation between the coronal cutoff energy and accretion parameters such as the Eddington ratio and black hole mass. We also do not find a statistically significant correlation between the X-ray photon index, {Gamma}, and Eddington ratio. This calls into question the use of such relations to infer properties of supermassive black hole systems.