In this work we study the symmetry-energy coefficient of neutron-rich nuclei,and the temperature dependence of nuclear symmetry energy at low temperatures.An isobaric method is used to extract the symmetry-energy coefficients of neutron-rich nucleus(asym) at zero temperature(T) and asym/T at nonzero temperature in the measured 1A GeV124,136Xe+Pb reactions.T of fragment is obtained from the ratio of its asym to asym/T.The results show that,for fragment with the same neutron-excess(I=N Z),the heavier the fragment is,the higher T it has,and T tends to saturate around 1 MeV for the large mass fragments.It is also shown that the more neutron-rich the isobar is,the higher temperature it has.The T2dependence of symmetry energy of finite nucleus at low temperatures is verified by the extracted results.