Context. Planet formation starts around Sun-like protostars with ages ≤ 1 Myr: what is the chemical compositions in disks? Aims. To trace the radial and vertical spatial distribution of H 2 CS, a key species of the S-bearing chemistry, in protoplanetary disks. To analyse the observed distributions in light of the H 2 CS 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-H 2 CS(7 1,6 − 6 1,5) line. ALMA-Band 6 was used, reaching spatial resolutions 40 au, i.e. Solar System spatial scales. We also estimated the binding energy of H 2 CS using quantum mechanical calculations, for the first time, for an extended, periodic, crystalline ice. Results. We imaged H 2 CS emission in two rotating molecular rings in the HL Tau and IRAS04302+2247 disks. The outer radii are ∼ 140 au (HL Tau), and 115 au (IRAS 04302+2247). The edge-on geometry of IRAS 04302+2247 allows us to reveal that H 2 CS emission peaks, at radii of 60-115 au, at z = ± 50 au from the equatorial plane. Assuming LTE conditions, the column densities are ∼ 10 14 cm −2. Upper limits of a few 10 13 cm −2 have been estimated for the H 2 CS column densities in DG Tau, DG Tau B, and Haro 6-13 disks. For HL Tau, we derive, for the first time, the [H 2 CS]/[H] abundance in a protoplanetary disk (10 −14). The binding energy of H 2 CS computed for extended crystalline ice and amorphous ices is 4258 K and 3000-4600 K, respectively, implying a thermal evaporation where dust temperature is ≥ 50-80 K. Conclusions. H 2 CS traces the so-called warm molecular layer, a region previously sampled using CS, and H 2 CO. Thioformaldehyde peaks closer to the protostar than H 2 CO and CS, plausibly due to the relatively high-excitation level of observed 7 1,6 − 6 1,5 line (60 K). The H 2 CS binding energy implies that thermal desorption dominates in thin, au-sized, inner and/or upper disk layers, indicating that the observed H 2 CS emitting up to radii larger than 100 au is likely injected in the gas due to non-thermal processes.