  The superconducting-state heat capacity of
Na$_{0.3}$CoO$_{2}$$\cdot$1.3H$_{2}$O shows unusual, marked deviations from BCS
theory, at all temperatures. At low temperatures the heat capacity has the
$T^2$ dependence characteristic of line nodes in the energy gap, rather than
the exponential temperature dependence of a fully gapped, conventional
superconductor. At temperatures of the order of one fifth of the critical
temperature and above, the deviations are strikingly similar to those of
MgB$_2$, which are known to be a consequence of the existence of substantially
different energy gaps on different sheets of the Fermi surface. A two-gap fit
to the Na$_{0.3}$CoO$_{2}$$\cdot$1.3H${_2}$O data gives gap amplitudes of 45%
and 125% of the BCS value, on parts of the Fermi surface that contribute,
respectively, 45% and 55% to the normal-state density of states. The
temperature of the onset of the transition to the vortex state is independent
of magnetic field, which shows the presence of unusually strong fluctuations.
