Based on the fundamental theory of heat transfer, the mathematical formulas that describing the transient temperature distributions of two-sided laser diode (LD) pumped Nd∶GGG (gadolinium gallium garnet) heat capacity slab laser were derived in this paper. By means of finite element analysis by ANSYS, transient temperature fields and stress distribution in the slab medium were simulated with various boundary conditions, while the beam distortions induced by thermal gradients were analyzed briefly. The obtained results could benefit to the primary designing of solid state heat capacity laser (SSHCL). Numerical analysis proved that under incomplete adiabatic boundary conditions, it would result in temperature gradients perpendicular to the optical axis. About 0.2 μm optical path differences would occur between the edge and optical axis of the slab. In addition, the thermal distributions in the slab during the subsequent cooling stage were mainly studied. The influences of different cooling methods such as air cooling, water cooling and mist cooling were discussed and cooling methods suitable for a SSHCL were briefly studied.