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Summary form only given. In the present report on the base of kinetic fluctuations theory the relaxation process between the electron and ion temperatures in a magnetized inhomogeneous plasma with density gradient is considered, the case when the external pump wave excites the lower hybrid and the electron drift waves is investigated. In the region above the instability threshold (the turbulent plasma state) it is found that the inverse relaxation time grows with increasing density gradient and pump wave intensity, Thus the presence of parametric instability leads to the relaxation time decrease, i.e. the velocity of the HF plasma heating grows.