Based on the theory of semi-analytical thermal analysis,the thermal effects within a laser diode (LD)-end-pumped Nd:YAG microchip crystal with back surface cooling are investigated. Through the working characteristics analysis of Nd:YAG microchip crystal that is pumped by a LD with a Gaussian distribution,a thermal model is established. The temperature field in the microchip Nd:YAG crystal is obtained by a novel solution to solve the third find heat conduction equation with Dini series,and the influence of air heat transfer coefficient on the temperature rise in the crystal is researched. Research results show that a maximum temperature rise of 70.17 ℃ and a maximum thermal distortion of 0.836 μm occur in the center of the pump face when the total pump power is 24.2 kW. These results can provide basis for the optimized design of LD-end-pumped microchip laser with back surface cooling.