  We extend a recent three-loop calculation of nuclear matter in the systematic
framework of chiral perturbation theory to finite temperatures T. The
contributions from one- and two-pion exchange diagrams which cause nuclear
binding and saturation at T=0 are included for T>0 in the density and
temperature dependent free energy per particle, $\bar F(rho,T)$. The so-called
anomalous 2pi-exchange contribution $\bar A(rho,T)$ (with no counterpart in the
ground state energy density at T=0) is consistently included. The calculated
pressure isotherms display the familiar first-order liquid-gas phase transition
of isospin symmetric nuclear matter with a critical point at T_c = 25.5 MeV and
rho_c = 0.09 fm^{-3}. The too high value of the critical temperature originates
from the strong momentum dependence of the underlying single-particle potential
U(p,k_{f0}) near the Fermi-surface. We also consider pure neutron matter at T>0
in the same framework and find fair agreement with sophisticated many-body
calculations for neutron densities rho_n < 0.2 fm^{-3}.
