  The formalism of next-to-leading order Fermi Liquid Theory is employed to
calculate the thermal properties of symmetric nuclear and pure neutron matter
in a relativistic many-body theory beyond the mean field level which includes
two-loop effects. For all thermal variables, the semi-analytical
next-to-leading order corrections reproduce results of the exact numerical
calculations for entropies per baryon up to 2. This corresponds to excellent
agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In
addition to providing physical insights, a rapid evaluation of the equation of
state in the homogeneous phase of hot and dense matter is achieved through the
use of the zero-temperature Landau effective mass function and its derivatives.
