  We investigate the electronic properties and the superconducting gap
characteristics of a single crystal of hole-doped 122 Fe-pnictide
Ba$_{0.65}$Na$_{0.35}$Fe$_2$As$_2$ by means of specific heat measurements. The
specific heat exhibits a pronounced anomaly around the superconducting
transition temperature $T_c$ = 29.4 K, and a small residual part at low
temperature. In a magnetic field of 90 kOe, the transition is broadened and
$T_c$ is lowered insignificantly by an amount $\sim$ 1.5 K. We estimate a high
electronic coefficient in the normal state with a value 57.5 mJ mol$^{-1}$
K$^2$, being consistent with hole-doped 122 compounds. The
temperature-dependent superconducting electronic specific heat cannot be
described with single-gap BCS theory under weak coupling approach. Instead, our
analysis implies a presence of two s-wave like gaps with magnitudes
$\Delta_1(0)/k_BT_c$ = 1.06 and $\Delta_2(0)/k_BT_c$ = 2.08 with their
respective weights of 48% and 52%. While our results have qualitative
similarities with other hole-doped 122 materials, the gap's magnitude and their
ratio are quite different.
