Heat-hydraulic design studies of the low-temperature sub-system of the ultracold neutron (UCN) supersource at the WWR-M reactor have been presented in the paper. The studies were directed toward selection of the optimal working modes of the aggregate technological complex of this source. According to the calculation data, the Linde TCF-50 standard refrigerator was able to maintain the operating temperature of the thermal screens and the condensation of 50 liters of the deuterium pre-moderator in the chamber. Calculation results for the temperature field of the thermal shield placed in the low-temperature sub-system were used to select the location of the support structures for a superfluid helium vessel. Based on these calculations, an estimate of the total heat penetration at the UCN source chamber was made; it was equal to 35W. The capacity of the vacuum system for pumping the helium vapor and helium liquefier was established to be sufficient to maintain 35 liters of the superfluid UCN converter.