We grew the single crystals of the SnAs-based van der Waals (vdW)-type superconductor NaSn$_2$As$_2$ and systematically measured its resistivity, specific heat, and ultralow-temperature thermal conductivity. The superconducting transition temperature $T_c$ = 1.60 K of our single crystal is 0.3 K higher than that previously reported. A weak but intrinsic anomaly situated at 193 K is observed in both resistivity and specific heat, which likely arises from a charge-density-wave (CDW) instability. Ultralow-temperature thermal conductivity measurements reveal a fully-gapped superconducting state with a negligible residual linear term in zero magnetic field, and the field dependence of $kappa_0 / T$ further suggests NaSn$_2$As$_2$ is an $s$-wave superconductor.
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