The Active Galactic Nuclei (AGN) produce copious amounts of X-rays through the corona that is the hot gas that lies close to the accretion disk. The temperature of the corona can be accurately determined by the cut-off signature in the X-ray spectrum. Owing to the large temperatures of the corona, observations well above 10 keV are necessary. Here, we explore the NuSTAR observations of 118 Gehrels/Swift selected Seyfert 1 AGN. We model the spectrum using a single power-law with an exponential cut-off modified by neutral and ionised absorption as well as a reflection component. We find secure spectral cut-off estimates in 62 sources while for the remaining ones we derive only lower limits. The mean value is 103 keV with a skewed distribution towards large energies with large dispersion. When we consider the lower limits using survival analysis techniques, the mean cut-off energy becomes significantly larger, about 200 keV. Because of various limitations (e.g. limited spectral passband, photon statistics, model degeneracies) we perform extensive simulations to explore the underlying spectral cut-off distribution. We find that an intrinsic spectral cut-off distribution which has a Maxwell-Boltzmann shape with a mean value in the range of 160 - 200 keV can reproduce sufficiently well the observations. Finally, our spectral analysis places very stringent constraints on both the photon index (Gamma=1.77+/-0.01) as well as on the reflection component (R=0.69+/-0.04) of the Seyfert 1 population. From the values of the spectral cut-off and the photon-index we deduce that the mean optical depth of the AGN corona is approximately tau=1.82+/-0.14 and its mean temperature approximately kT=65+/-10 keV.
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