  We consider a higher-dimensional hard wall model with an infrared (IR)
cut-off in asymptotically AdS space and investigate its thermodynamics via the
holographic renormalization method. We find a relation between the confinement
temperature and the IR cut-off for any dimension. It is also shown that the
entropy of $p$-branes with the number of coincident branes (the number of the
gauge group) $N$ jumps from leading order in $\cal O$($N^0$) at the confining
low temperature phase to $\cal O$($N^{\frac{p+1}{2}}$) at the deconfining high
temperature phase like $D3$-branes ($p=3$) case. On the other hand, we
calculate the configuration entropy (CE) of various magnitudes of an inverse
temperature at an given IR cut-off scale. It is shown that as the inverse
temperature grows up, the CE above the critical temperature decreases and AdS
black hole (BH) is stable while it below the critical temperature is constant
and thermal AdS (ThAdS) is stable. In particular, we also find that the CE
below the critical temperature becomes constant and its magnitude increases as
a dimension of AdS space increases.
