  Asymmetric nuclear matter equation of state at finite temperature is studied
in SU(2) chiral sigma model using mean field approximation. The effect of
temperature on effective mass, entropy, and binding energy is discussed.
Treating the system as one with two conserved charges the liquid-gas phase
transition is investigated. We have also discussed the effect of proton
fraction on critical temperature with and without $\rho$-meson contribution. We
have extended our work to study the structure of proto-neutron star with
neutron free charge-neutral matter in beta-equilibrium. We found that the mass
and radius of the star decreases as it cools from the entropy per baryon S = 2
to S = 0 and the maximum temperature of the core of the star is about 62 MeV
for S = 2.
