  This work aim to study the various thermal characteristics of nuclei in view
of the saturation and critical behavior of infinite nuclear matter. The free
energy of a nucleus is parametrized using the density and temperature-dependent
liquid-drop model and interaction among nucleons is worked out within the
effective relativistic mean-field theory (E-RMF). The effective mass (m,$^*$)
and critical temperature of infinite symmetric nuclear matter ($T_c$) of a
given E-RMF parameter force play a seminal role in the estimation of thermal
properties. A larger (m$^*$) and $T_c$ of the E-RMF set estimate larger
excitation energy, level density, and limiting temperature $(T_l)$ for a given
nucleus. The limiting temperature of a nucleus also depends on the behavior of
the nuclear gas surrounding the nucleus, making the equation of state (EoS) at
subsaturation densities an important input. A stiff EoS in the subsaturation
region estimates a higher pressure of the nuclear gas making it less stable.
Since the $T_c$ plays an important part in these calculations, we perform a
Pearson correlation statistical study of fifteen E-RMF parameter sets,
satisfying the relevant constraint on EoS. Effective mass seems to govern the
thermal characteristics of infinite as well as finite nuclear matter in the
framework of E-RMF theory.
