Based on the fundamental theory of heat transmission, the transient thermal and stress distributions of laser gain medium in a laser diode end-pumped Nd doped glass disk amplifier are studied by means of finite element analysis. The cooling characteristics of glass disk on different boundary conditions in repetition mode are also discussed. Furthermore, three kinds of different thermal management schemes are proposed with the progress and their thermal effect characteristics are compared. The simulation results show that the cooling configuration with transparent sapphire plate adjacent to the pumping surface which is mounted with TEC-cooled copper housing outside is much attractive. The peak temperature about 120℃ occurs in the centre of non-pumping surface. Although its cooling ability is not much effective as that of direct water cooling but it can avoid some problems brought out by the latter. The simulation analysis also proves that the heat within glass disk is difficult to be taken away radially because of its large heat resistance. In practice, the thermal management system should be designed to cool glass disk along axis direction.