A physical model was established to study the distribution and change of temperature field of Nd∶ GGG disc operated under heat-capacity mode. By using heat conducting equation and Green function,the expressions of temperature field inside the crystal were obtained during the operation and cooling period of the laser;the obtained data reflect the change of temperature filed. The temperature field was calculated after the crystal was pumped as long as 4 s under the pump conditions(rectangular LD facula 3 cm,power 8.1 kW,frequency 500 Hz,width 0.2 ms),and the maximal stress is up to 47% of the crystal rupture limit at the end of 4 s. The cooling time is about 60～70 s when the back of the disc is cooled at the temperature 280 K and 290 K respectively;the cooling time is shorted to be about 30 s when both the back and side of disc were cooled at the temperature 280 K.