  Comprehensive low-temperature specific heat data C(T,H) of
Na_0.35CoO2-1.3H_2O with temperature T down to 0.6 K and the magnetic field H
up to 8 T are presented. For the normal state, the values of gamma_n=13.94
mJ/mol K2, and Debye temperature 362 K are reported. At zero field, a very
sharp superconducting anomaly was observed at Tc=4.5 K with
DeltaC/gamma_nTc=1.45. The superconducting volume fraction is estimated to be
47.4 % based on the consideration of entropy balance at Tc for the second-order
superconducting phase transition. In the superconducting state, the electronic
contribution C_es at H=0 can be well described by the model of the line nodal
order parameter. In low H, gamma(H) H^1/2 which is also a manifestation of the
line nodes. The behaviors of both Tc(H) and gamma(H) suggest the anisotropy of
Hc2 or possible crossovers or transitions occurring in the mixed state.
