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Aims: To trace the radial and vertical spatial distribution of H2CS, a key species of the S-bearing chemistry, in protoplanetary disks. To analyse the observed distributions in light of the H2CS binding energy, in order to discuss the role of thermal desorption in enriching the gas disk component. Methods: In the context of the ALMA chemical survey of Disk-Outflow sources in the Taurus star forming region (ALMA-DOT), we observed five Class I or early Class II sources with the o-H2CS(7_1,6-6_1,5) line on a 40 au scale. We estimated the binding energy (BEs) of H2CS using quantum mechanical calculations, for the first time, for an extended, periodic, crystalline ice. Results: We imaged H2CS in two rotating molecular rings in the HL Tau and IRAS04302+2247 disks. The outer radii are about 140 au (HL Tau), and 115 au (IRAS 04302+2247). The edge-on geometry of IRAS 04302+2247 reveals that H2CS emission peaks, at radii of 60-115 au, at z = +- 50 au from the equatorial plane. The column densities are about 10^14 cm^-2. For HL Tau, we derive, for the first time, the [H2CS]/[H] abundance in a protoplanetary disk (about 10^-14). The BEs of H2CS computed for extended crystalline ice and amorphous ices is 4258 K and 3000-4600 K, respectively, implying a thermal evaporation where dust temperature is larger than 50-80 K. Conclusions: H2CS traces the so-called warm molecular layer, a region previously sampled using CS, and H2CO. Thioformaldehyde peaks closer to the protostar than H2CO and CS, plausibly due to the relatively high-excitation level of observed 7_1,6-6_1,5 line (60 K). The H2CS BEs implies that thermal desorption dominates in thin, au-sized, inner and/or upper disk layers, indicating that the observed H2CS emitting up to radii larger than 100 au is likely injected in the gas due to non-thermal processes.