  We present systematic and uniform analysis of NuSTAR data with 10-78 keV S/N
> 50, of a sample of 60 SWIFT BAT selected AGNs, 10 of which are radio-loud. We
measure their high energy cutoff Ecut or coronal temperature Te using three
different spectral models to fit their NuSTAR spectra, and show a threshold in
NuSTAR spectral S/N is essential for such measurements. High energy spectral
breaks are detected in the majority of the sample, and for the rest strong
constraints to Ecut or Te are obtained. Strikingly, we find extraordinarily
large Ecut lower limits ( > 400 keV, up to > 800 keV) in 10 radio-quiet
sources, whereas none in the radio-loud sample. Consequently and surprisingly,
we find significantly larger mean Ecut/Te of radio-quiet sources compared with
radio-loud ones. The reliability of these measurements are carefully inspected
and verified with simulations. We find a strong positive correlation between
Ecut and photon index {\Gamma}, which can not be attributed to the parameter
degeneracy. The strong dependence of Ecut on {\Gamma}, which could fully
account for the discrepancy of Ecut distribution between radio-loud and
radio-quiet sources, indicates the X-ray coronae in AGNs with steeper hard
X-ray spectra have on average higher temperature and thus smaller opacity.
However, no prominent correlation is found between Ecut and {\lambda}edd. In
the l-{\Theta} diagram, we find a considerable fraction of sources lie beyond
the boundaries of forbidden regions due to runaway pair production, posing
(stronger) challenges to various (flat) coronal geometries.
