WWR-K (Water-Water Reactor - Kazakhstan) was restarted after a major modernization related to its conversion to low enriched uranium (LEU) fuel and has been operating on LEU fuel since September 2016. The reactor, built in 1967, has been significantly modernized to meet modern safety requirements. This important neutron source in Kazakhstan serves various purposes, such as basic and applied research in physics, chemistry, biology, materials science, as well as for radiation treatment of materials and production of radioisotopes. It is also used for training. Instrumentation projects are planned to be launched on the basis of the WWR-K reactor to install a basic set of experimental stations. Significant efforts will be made to develop an ultracold neutron (UCN) source, which will expand research capabilities. For this purpose, it is proposed to use the niche of thermal column, a large diameter horizontal channel that allows irradiation of objects up to 1000 mm in size. In addition, the niche of thermal column has four radial channels that can be used to extract cold (10−6–10−3 eV) and very cold (10−7–10−6 eV) neutrons. The paper presents calculations of spatial and energy distributions of neutron and gamma fields for the current and for the additional moderator configuration of the niche of thermal column of the WWR-K reactor. It is shown that the configuration with additional moderator does not lead to an increase in the slow neutron fields (<1 eV), and the existing moderator thickness is optimal.