  We use density functional molecular dynamics (DFT-MD) to study the effect of
finite temperature exchange-correlation (xc) in Hydrogen. Using the Kohn-Sham
approach, the xc energy of the system, $E_{xc}(r_{s})$ is replaced by the xc
free energy $f_{xc}(r_{s},\Theta)$ within the local density approximation (LDA)
based on parametrized path integral Monte Carlo (PIMC) data for the uniform
electron gas (UEG) at warm dense matter (WDM) conditions. We observe
insignificant changes in the equation of state (EOS) at the region of
metal-insulator transition compared to the regular LDA form, whereas
significant changes are observed for T$>$10000 K, i.e., in the important WDM
regime. Thus, our results further corroborate the need for
temperature-dependent xc functionals for DFT simulations of WDM systems.
Moreover, we present the first finite-temperature DFT results for the EOS of
Hydrogen in the electron liquid regime up to $r_{s}=14$ and find a drastic
impact (about $20\%$) of thermal xc effects, which manifests at lower
temperatures compared to WDM. We expect our results to be important for many
applications beyond DFT, like quantum hydrodynamics and astrophysical models.
