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We have developed and tested a zinc superconducting heat switch suitable for magnetic refrigeration and calorimetric experiments at sub-millikevin (sub-mK) temperatures. The specific application here is an adiabatic demagnetization refrigerator with two PrNi$_{5}$ nuclear stages, which can keep a temperature of 0.8 mK continuously, (CNDR) proposed by Toda et al. (J. Phys.: Conf. Ser. 969, 012093 (2018). The switch consists of six high-purity zinc foils of 0.25 mm thick which contact seven silver foils by diffusive bonding. The silver foils are electron beam welded to silver rods that are thermal links to other components. The choice of the thin zinc foils is due to reduce the magnetic latent heat on switching and the contact thermal resistance under a constraint on the aspect ratio of the switch element. The measured thermal conductance of the whole switch assembly in the normal (closed) state, $K_\mathrm{closed}$, agrees very well down to 70 mK with the value estimated from the residual electrical resistance 114 n$\mathrmΩ$ at 4.2 K, indicating the validity of the Wiedemann-Franz law for zinc. The measured thermal conductance in the superconducting (open) state, $K_\mathrm{open}$, follows nicely the prediction from the BCS theory and approaches the value expected from the Debye model for thermal phonons near 70 mK. The heat leak through the HSW from the higher temperature side of 30 mK at most is estimated to be less than 0.5 nW, which is much lower than the expected cooling power ($= 10$ nW) of the CNDR at 0.8 mK . The switching ratio $K_\mathrm{closed}/K_\mathrm{open}$ extrapolated to 30 mK, is as high as 5$\times10^4$. All the test results meet the requirements for the CNDR and, for example, heat capacity measurements at sub-mK.