Zinc oxide (ZnO) is a very promising material for optoelectrical devices operating at the short-wavelength end of the visible spectral range and at the near UV. The Raman scattering studies of ZnO heterolayers formed by isothermal annealing show sharp phonon lines. In addition to the A_1(TO), E_1(TO), E_2^{H}, and E_1(LO) one-phonon lines, we observed two-phonon lines identified as: E_2^{H} - E_2^{L}, E_2^{H} + E_2^{L}, and 2LO at 332, 541, and 1160 cm^{-1}, respectively (at room temperature). The identification of the E_2^{H} - E_2^{L} peak was confirmed by its thermal dependence. Temperature dependent measurements in the range 6-300 K show that the phonon frequencies decrease with temperature. The E_2^{H} peak is at energy 54.44 meV (439.1 cm^{-1}), at 4 K and due to phonon-phonon anharmonic interaction, its energy decreases to 54.33 meV (438.2 cm^{-1}) at room temperature. The Grüneisen parameter found for this oscillation mode was γ_{E} 2H = 1.1 at about 300 K. The intensity of the E_2^{H} - E_2^{L} peak increases strongly with temperature and this dependence can be described by the Bose-Einstein statistics with activation energy of 13.8 meV (nearly equal to the energy of the E_2^{L} phonon).