  The prediction of the equation of state of hot, dense nuclear matter is one
of the most complicated and interesting problems in nuclear astrophysics. At
the same time, knowledge of it is the basic ingredient for some of the most
interesting studies. In the present work, we concentrate our study on the
construction of the equation of state of hot, dense nuclear matter, related
mainly to the interior of the neutron star. We employ a theoretical nuclear
model, which includes momentum-dependent interaction among the nucleons, along
with the \textit{state-of-the-art} microscopic calculations. Thermal effects
are introduced in a self-consistent way, and a set of isothermal and isentropic
equations of state are predicted. The predicted equations of state are used in
order to acquire and to extend the knowledge of the thermal effect on both
nonrotating and rapidly rotating with the Kepler frequency neutron stars. The
simultaneous study of thermal and rotation effects provides useful information
on some of the most important quantities, including the mass (gravitational and
baryon) and radius, the Kepler frequency and Kerr parameter, the moment of
inertia, etc. These quantities are directly related to studies of protoneutron
stars and mainly the hot and rapidly rotating remnant of a binary neutron star
merger. Data from the late observations of binary neutron star mergers and the
present study may offer useful tools for their investigation and help in
providing possible constraints on the equation of state of nuclear matter.
