Although NaOH and NaOD exhibit parallel polymorphism at high temperatures, NaOD exhibits a low-temperature phase transition to a hydrogen-bonded antiferroelectric phase and no comparable transition has been found in NaOH. Measurements of NaOH by dielectric relaxation and adiabatic calorimetry were undertaken to determine if proton disorder becomes frozen in NaOH at low temperatures. No evidence for relaxation in NaOH was found from calorimetry or dielectric measurements. A comparison of the low-temperature heat capacities of NaOH and NaOD showed that NaOH has excess heat capacity, likely due to the existence of tunneling levels, and this was satisfactorily fit to a two-level Schottky anomaly. Thus, hydrogen-atom ordering in NaOH appears to take place through a more gradual process at low temperatures, rather than a low-temperature phase transition as in NaOD. The difference in the behaviour of NaOH and NaOD likely is associated with oxygen-oxygen distances that are slightly longer in NaOH than in NaOD, owing to the different nature of higher-temperature dynamical disorder (classical-double-well potential for OD- and tunneling for OH-).