The three-dimensional (3D) pump intensity distribution in medium of the laser diode (LD) pumped high average power heat capacity laser is simulated by the ray tracing method, and the divergence characteristics of fast axis and slow axis of LD are simultaneously considered. The transient 3D temperature and stress distributions are also simulated by the finite element method (FEM) with considering the uneven heat source distribution in medium. A LD face-pumped Nd:GGG heat capacity laser is designed. The average output power is 1.49 kW with an optical-optical efficiency of 24.1%.