Results of the analysis of variations of the proton temperature anisotropy (A) across the magnetosheath along with some plasma wave turbulence characteristics are discussed. It is shown that the deviation of the observed values of A from the bounded anisotropy model may be explained by a finite value of the temperature isotropization time τ. In turn, the obtained values of τ have a tendency to decrease with the increase of the intensity of the magnetic field oscillations. The discovered dependence of τ on the intensity of mirror-wave-like turbulence seems to confirm the supposition by Hill et al. <1995> on a significant role of mirror waves in the pitch angle scattering of protons in the magnetosheath plasma. It is shown that the observed periods of abnormally low values of A in some cases correspond to the periods of relatively high intensive magnetic field oscillations, most probably of an external origin.