  The free energy and the equation of state of isospin-asymmetric nuclear
matter are calculated at finite temperature up to three loop order in the
framework of in-medium chiral perturbation theory, systematically incorporating
one- and two-pion exchange dynamics to this order. Effects from the two-pion
exchange with explicit {\Delta}-isobar excitation are included, as well as
three-body forces. We construct the phase diagram of nuclear matter for
different proton fractions x_p and investigate the dependence of nuclear matter
properties on the isospin-asymmetry. A detailed study of the liquid-gas phase
transition is performed. For isospin-symmetric nuclear matter we find a
critical temperature of 15.1 MeV; as the isospin-asymmetry is increased, the
liquid-gas coexistence region decreases until it disappears at x_p \approx
0.05, while nuclear matter becomes unbound at x_p \approx 0.12. The quadratic
expansion of the free energy in the asymmetry parameter {\delta} is a good
approximation at low temperature even for large {\delta}. An estimate of chiral
four-body correlations in nuclear and neutron matter is also performed and the
corrections from such four-body interactions are found to be small.
