A depolarization phenomenon in an electro-optical crystal in a quasi-three-level 946 nm Nd:YAG laser is observed. A compensation of the thermal effects in electro-optical crystals is achieved by employing a quarter-wave plate, with one optical axis parallel to the laser polarization. This technique allows for the production of an electro-optically Q-switched 946 nm Nd:YAG laser at 1 kHz. A maximum output power of 350 mW at 1 kHz repetition frequency and 11 ns pulse duration are achieved with an output coupler of 10% transmission under the incident pump power of 11.1 W, corresponding to a peak power of ～32 kW.