  We present first-principle predictions for the liquid-gas phase transition in
symmetric nuclear matter employing both two- and three-nucleon chiral
interactions. Our discussion focuses on the sources of systematic errors in
microscopic quantum many body predictions. On the one hand, we test
uncertainties of our results arising from changes in the construction of chiral
Hamiltonians. We use five different chiral forces with consistently derived
three-nucleon interactions. On the other hand, we compare the ladder
resummation in the self-consistent Green's functions approach to finite
temperature Brueckner--Hartree--Fock calculations. We find that systematics due
to Hamiltonians dominate over many-body uncertainties. Based on this wide pool
of calculations, we estimate that the critical temperature is $T_c=16 \pm 2$
MeV, in reasonable agreement with experimental results. We also find that there
is a strong correlation between the critical temperature and the saturation
energy in microscopic many-body simulations.
