  We study if commonly used nucleon-nucleon effective interactions, obtained
from fitting the properties of cold nuclear matter and of finite nuclei, can
properly describe the hot dense nuclear matter produced in intermediate-energy
heavy-ion collisions. We use two representative effective interactions, i.e.,
an improved isospin- and momentum-dependent interaction with its isovector part
calibrated by the results from the \emph{ab initio} non-perturbative
self-consistent Green's function (SCGF) approach with chiral forces, and a
Skyme-type interaction fitted to the equation of state of cold nuclear matter
from chiral effective many-body perturbation theory and the binding energy of
finite nuclei. In the mean-field approximation, we evaluate the equation of
state and the single-nucleon potential for nuclear matter at finite
temperatures and compare them to those from the SCGF approach. We find that the
improved isospin- and momentum-dependent interaction reproduces reasonably well
the SCGF results due to its weaker momentum dependence of the mean-field
potential than in the Skyrme-type interaction. Our study thus indicates that
effective interactions with the correct momentum dependence of the mean-filed
potential can properly describe the properties of hot dense nuclear matter and
are thus suitable for use in transport models to study heavy-ion collisions at
intermediate energies.
