This report describes self-regulating properties of the Kyoto University Reactor (KUR) Cold Neutron Source (CNS), which is cooled by a closed-thermosiphon loop of hydrogen, as are most of the CNS constructed recently. The circular moderator transfer tube is in a plane inclined about 14° to the horizontal plane. The hydrogen-helium cryogenic system of the CNS shows a self-regulating characteristic under thermal disturbances, if they are smaller than about 30% of the practical allowable heat load, 300 W at 25 K in our case. This self-regulating characteristic has been confirmed from Bode's diagram of the hydrogen pressure response in the reservoir tank to the heat load modulation. Due to this property, the liquid level in the moderator cell is kept almost constant during long term operation of the reactor. Measurements of the vertical distribution of the cold neutron flux from the moderator cell showed that a sufficient amount of liquid was stored in the cell and the ratio of the fraction of cold neutrons in the cold moderator to that in the ambient moderator was measured to be about 20 where the wavelengths are longer than 6 Å using liquid hydrogen as a moderator.