  We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm
dense uniform electron gas in the thermodynamic limit. By combining QMC data
with linear response theory we are able to remove finite-size errors from the
potential energy over the entire warm dense regime, overcoming the deficiencies
of the existing finite-size corrections by Brown \emph{et al.}~[PRL
\textbf{110}, 146405 (2013)]. Extensive new QMC results for up to $N=1000$
electrons enable us to compute the potential energy $V$ and the
exchange-correlation free energy $F_{xc}$ of the macroscopic electron gas with
an unprecedented accuracy of $|\Delta V|/|V|, |\Delta F_{xc}|/|F|_{xc} \sim
10^{-3}$. A comparison of our new data to the recent parametrization of
$F_{xc}$ by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals
significant deviations to the latter.
