We report the results of an investigation of the temperature dependence of the magnon and phonon frequencies in NiO. A combination of Brillouin-Mandelstam and Raman spectroscopies allowed us to elucidate the evolution of the phonon and magnon spectral signatures from the Brillouin zone center (GHz range) to the second-order peaks from the zone boundary (THz range). The temperature-dependent behavior of the magnon and phonon bands in the NiO spectrum indicates the presence of antiferromagnetic (AF) order fluctuation or a persistent AF state at temperatures substantially above the Néel temperature (TN=523 K). Tuning the intensity of the excitation laser provides a method for disentangling the features of magnons from acoustic phonons in AF materials without the application of a magnetic field. Our results are useful for the interpretation of the inelastic-light scattering spectrum of NiO and add to the knowledge of its magnon properties important for THz spintronic devices.