  Recent studies have revealed that certain nuclear parameters are more
dominant than others in governing global neutron star properties, such as its
structure or oscillation mode characteristics. Although neutron stars can in
general assumed to be cold, in astrophysical scenarios such as newly born
neutron stars or remnants of binary neutron star mergers, finite temperature
effects play a non-negligible role. In this work, we perform a consistent and
systematic investigation of the role of nuclear parameters and thermal effects
on neutron star properties and fluid oscillation modes within a full general
relativistic scheme. We impose constraints on the parameter space of the
relativistic mean field model using state-of-the-art information from
terrestrial experiments and multi-messenger astrophysical data. We find
effective nucleon mass to be the most important nuclear parameter controlling
astrophysical observables of hot neutron stars, similar to the cold beta
equilibrated matter. However, we conclude that the interplay among saturation
properties and astrophysical observables depends not only on the thermal
configurations considered but also on the constraints imposed. We also
investigated the role of nuclear saturation parameters on some universal
relations for hot NSs which are important in gravitational wave
asteroseismology. Our investigation confirmed that these relations are mostly
insensitive to nuclear saturation properties and mainly affected by variation
of charge fraction in the star.
