Active galactic nuclei (AGN) are extremely variable in the X-ray band down to very short time scales. However, the driver of the X-ray variability is still poorly understood. Previous results suggest that the hot corona, which is responsible for the primary Comptonized emission observed in AGN, should have 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 ($\tau$). We present the spectral and timing analysis of 46 NuSTAR observations corresponding to a sample of 20 AGN. For each source we derive the coronal temperature and optical depth through X-ray spectroscopy, and we compute the normalized excess variance for different energy bands at a time scale of $10$ ks. We find a strong inverse correlation between $kT$ and $\tau$, with correlation coefficient $r<-0.9$ and negligible null probability. No clear dependence between the temperature and physical properties such as the black hole mass and the Eddington ratio is found. We also find that the observed X-ray variability does not correlate with either the coronal temperature or optical depth under the thermal equilibrium assumption, while it is anti-correlated with the black hole mass. These results can be interpreted in a scenario where one possibility is that the observed X-ray variability could be mainly driven by variations in coronal physical properties on a time scale of less than $10$ ks, whereas we assume thermal equilibrium at such time scales in this paper, given the capability of the currently available hard X-ray telescopes. However, 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 by its physical properties.