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A several-kilowatt level laser at 946 nm is demonstrated in a cryogenically cooled diode-pumped Nd:YAG slab system. The oscillator realizes the record of the output power of 2.85 kW in a compact cavity with the homemade cryogenically cooled Nd:YAG crystal slab. The pulse repetition rate and pulse width of the laser are 400 Hz and 200 µs, respectively, and the center wavelength under full power is 946.2 nm with a bandwidth of about 0.5 nm. The absorption linewidth at 808 nm is a little narrowed and blue shifts at the cryogenic temperature, while the cooling temperature decreases from 300 to 77 K. The measured thermal conductivity increases from 10 to 70 W/mˑK, and the thermal expansion coefficient decreases from 7.5*10−6 to 1.5*10−6/K. These results could guide us in simulating the temperature gradient and thermal-induced stress distributions in the crystal slab.