In order to solve the problem that the heat capacity laser pumped by laser diode generate a large amount of waste heat inside the crystal during the pumping stage, a thermal model of Yb∶YAG composite crystal without cooling in the pumping stage and heat exchange between the face and air is established by the working characteristics of the LD end-pumped laser crystal. Based on the heat conduction theory, the temperature field, stress field and thermal deformation field of Yb∶YAG composite crystal are calculated by finite element method. The effects of bonding length and bonding mode on the temperature field and thermal deformation field are quantitatively analyzed. The results show that if a laser diode with a pumping power of 50 W and a pumping optical Gaussian radius of 300 μm is used to pump the end face of Yb∶YAG composite crystal with a crystal size of 3 mm×3 mm×4 mm, a bonding length of 1 mm, a bonding mode of single end bonding, and a doping concentration of 5.0 at. %, and the working time is 2 s, The maximum temperature rise of the internal field is 248 ℃, the maximum thermal shape variable is 5.9515 μm, and the maximum stress is 3.70395×10⁹ N/m². The research results provide a theoretical basis for the design of Yb∶YAG heat capacity laser pumped by laser diode end face.