  The evolution of the comoving kinetic luminosity densities
($\Omega_{\rm{kin}}$) of the radio loud (RL) high-excitation radio galaxies (RL
HERGs) and the low-excitation radio galaxies (LERGs) in the XXL-S field is
presented. The wide area and deep radio and optical data of XXL-S have allowed
the construction of the radio luminosity functions (RLFs) of the RL HERGs and
LERGs across a wide range in radio luminosity out to high redshift ($z = 1.3$).
The LERG RLFs display weak evolution: $\Phi (z)$ $\propto$ (1+$z$)$^{0.67 \pm
0.17}$ in the pure density evolution (PDE) case and $\Phi (z)$ $\propto$
(1+$z$)$^{0.84 \pm 0.31}$ in the pure luminosity evolution (PLE) case. The RL
HERG RLFs demonstrate stronger evolution than the LERGs: $\Phi (z)$ $\propto$
(1+$z$)$^{1.81 \pm 0.15}$ for PDE and $\Phi (z)$ $\propto$ (1+$z$)$^{3.19 \pm
0.29}$ for PLE. Converting $L_{\rm{1.4 GHz}}$ into kinetic luminosities, the
evolution of $\Omega_{\rm{kin}}$ was calculated for the RL HERGs and LERGs and
compared to the predictions from simulations. The prediction for the evolution
of radio mode feedback in the Semi-Analytic Galaxy Evolution model is
consistent with the $\Omega_{\rm{kin}}$ evolution for all XXL-S RL AGN,
indicating that RL AGN may be able to balance the radiative cooling of the hot
phase of the IGM. Simulations that predict the $\Omega_{\rm{kin}}$ evolution of
LERG equivalent populations show similar slopes to the XXL-S LERG evolution,
indicating that LERGs are well described by models of SMBHs that slowly accrete
hot gas. On the other hand, models of RL HERG equivalent populations differ in
their predictions. While LERGs dominate the kinetic luminosity output of RL AGN
at all redshifts, the evolution of the RL HERGs in XXL-S is weaker compared to
what other studies have found. This implies that radio mode feedback from RL
HERGs is more prominent at lower redshifts than was previously thought.
