Active galactic nuclei (AGN) are extremely variable in the X-ray band down to very short timescales. However, the driver behind the X-ray variability is still poorly understood. Previous results suggest that the hot corona responsible for the primary Comptonized emission observed in AGN is expected to play an important role in driving the X-ray variability. In this work, we investigate the connection between the X-ray amplitude variability and the coronal physical parameters; namely, the temperature ( kT ) and optical depth ( τ ). We present the spectral and timing analysis of 46 NuSTAR observations corresponding to a sample of 20 AGN. For each source, we derived the coronal temperature and optical depth through X-ray spectroscopy and computed the normalized excess variance for different energy bands on a timescale of 10 ks. We find a strong inverse correlation between kT and τ , with correlation coefficient of r < −0.9 and negligible null probability. No clear dependence was found among the temperature and physical properties, such as the black hole mass or the Eddington ratio. We also see that the observed X-ray variability is not correlated with either the coronal temperature or optical depth under the thermal equilibrium assumption, whereas it is anticorrelated with the black hole mass. These results can be interpreted through a scenario where the observed X-ray variability could primarily be driven by variations in the coronal physical properties on a timescale of less than 10 ks; whereas we assume thermal equilibrium on such timescales in this work, given the capability of the currently available hard X-ray telescopes. Alternatively, it is also possible that the X-ray variability is mostly driven by the absolute size of the corona, which depends on the supermassive black hole mass, rather than resulting from any of its physical properties.