On the basis of kinetic fluctuation theory, the relaxation process between the electron and ion temperatures in a magnetized inhomogeneous plasma is considered when an external pump wave parametrically decays into lower-hybrid and electron drift waves. In the region above the instability threshold, the inverse relaxation time is calculated, and its dependence on the density gradient and the pump-wave intensity and frequency is obtained. It is shown that the presence of the parametric instability leads to a decrease of the relaxation time.