Cavitation is physically "a vaporization of liquid" which needs latent heat for phase change. A cavity grows in the liquid, so the latent heat of vaporization can only be supplied by the liquid surrounding the cavity. Thus, the liquid close to the interface region of the cavity is cooled down. In general, cryogenic liquids are very thermosensitive. For liquid hydrogen and oxygen used in rocket propulsion, the temperature in the cavity, i.e., the vapor pressure in the cavity, is lower than those of the liquid bulk. Thanks to this thermal effect, cavitation in cryogenic liquids is less developed than that in water at room temperature. This thermal effect on cavitation is beneficial in that it improves cavitation performance and alleviates cavitation instability in space inducers. In previous works, we investigated the relationship between the thermodynamic effect and the cavitation instabilities, e.g., rotating cavitation and cavitation surge, with a focus on the cavity length as an indication of cavitation. In the present work, first, aspects of cavitation in the inducer were observed by direct optical visualization in liquid nitrogen. Second, joint experiments in liquid nitrogen and cold water were conducted on a cavitaing inducer. In nitrogen experiments, operating conditions, i.e., rotational speed and liquid temperature, were varied to determine the cavitation scaling law. Through these experimental results, characteristic times, namely, the transit time for bubble growth and the characteristic thermal time introduced from the thermal property, were investigated as a cavitation thermodynamic parameter. It was found out that the adjustment of cavitation number has a good correlation with the ratio of the transit time and the characteristic thermal time.