  We explore the thermal properties of hot and dense matter using a model that
reproduces the empirical properties of isospin symmetric and asymmetric bulk
nuclear matter, optical model fits to nucleon-nucleus scattering data,
heavy-ion flow data in the energy range 0.5-2 GeV/A, and the largest
well-measured neutron star mass of 2 $\rm{M}_\odot$. Results of this model
which incorporates finite range interactions through Yukawa type forces are
contrasted with those of a zero-range Skyrme model that yields nearly identical
zero-temperature properties at all densities for symmetric and asymmetric
nucleonic matter and the maximum neutron star mass, but fails to account for
heavy-ion flow data due to the lack of an appropriate momentum dependence in
its mean field. Similarities and differences in the thermal state variables and
the specific heats between the two models are highlighted. Checks of our exact
numerical calculations are performed from formulas derived in the strongly
degenerate and non-degenerate limits. Our studies of the thermal and adiabatic
indices, and the speed of sound in hot and dense matter for conditions of
relevance to core-collapse supernovae, the thermal evolution of neutron stars
from their birth and mergers of compact binary stars reveal that substantial
variations begin to occur at sub-saturation densities before asymptotic values
are reached at supra-nuclear densities.
