The process of transient thermal effect exists in pulsed laser diode (LD) end pumped solid state laser, which means that temperature distribution in laser crystal is changing with time. The process of time-varying temperature is influenced by thermal relaxation time. Based on the heat conduction equation, the characteristic of time-varying temperature in temperature declining process is calculated by analysis and numerical method. Based on the finite element method, the thermal relaxation time and its influencing factors are presented. The diameter, thermal parameters of crystal such as density, coefficient of heat conduction and specific heat are analyzed. Based on the theory of flow and heat transfer of water, influences of crystal temperature distribution such as temperature and velocity of cooling water are considered. The results show that thermal relaxation time can be controlled by changing diameter or cooling system. Based on the solution of ANSYS, time-varying temperature distribution, temperature difference and relative optical path difference between center and edge in pumped surface of crystal are analyzed. Focal length difference at different radii of the thermal lens is analyzed simply. The results indicate that in cooling process, temperature difference and relative optical path difference between center and other different radial positions are all changed with time; focus property of crystal thermal lens is also changed with time.