We report a detailed theoretical study of the thermal magnetic properties of the Ni sublattice in half-metallic NiMnSb. The study is performed in the temperature interval where the disordering of the Mn sublattice is weak and the properties of the Ni sublattice can play a crucial role. In earlier work it was suggested that the behavior of the Ni sublattice is responsible for the anomalies in the properties of NiMnSb detected experimentally atabout 80 K. Because of high Curie temperature T_C=730 K the interval of weak Mn disorder extends up to the technologically important room temperature. We formulate a thermodynamic model where both transversal and longitudinal fluctuations of the magnetic moments are taken into account. The energies of the fluctuations are determined by means of the constrained calculations within the framework of density-functional theory. We show that the half-metallicity is robust with respect to the longitudinal atomic fluctuations in the ground-state ferromagnetic structure. On the other hand the half-metallicity imposes strong restrictions on the longitudinal fluctuations. In contrast to longitudinal fluctuations the transversal fluctuations disturb the half-metallicity. We show that the contributions of the longitudinal and transversal fluctuations to the temperature dependence of the Ni net magnetization compensate, which leads to a very weak variation of the Ni magnetization in a broad temperature interval. This feature is in agreement with experiment. Simultaneously a large amplitude of the fluctuations results in strong decrease in the spin polarization of the Ni DOS at the Fermi level. The calculated temperature dependence of the Ni spin polarization reveals a crossover in the temperature interval between 75 and 100 K that correlates with experimental features in the temperature dependences of the physical properties. Although this crossover cannot be interpreted as the transition from a half-metallic to a non-half-metallic state the half-metallicity of the ground state is an important factor determining the properties of the fluctuations and the temperature properties.