Considering some necessary factors in the design of SSHCL, material properties of Nd doped glass, YAG and GGG were compared. Transient temperature fields and thermal stress in these slab mediums during one working cycle were simulated. Numerical analysis results showed that the internal external temperature difference in a neodymium doped glass slab was 75 K and the peak temperature value was 400 K when pumping time arrived 5 s. The maximum stress came to 50% of glass fracture limit. During subsequent water cooling period, the initial state was recovered after 120 s. On the same boundary conditions, Nd:YAG and Nd:GGG slabs could maintain relatively smooth temperature profile while the temperature rising and equivalent thermal stress were lower compared to glass. In later cooling phase, both of them could reach their operating commencement within 30 s. As cooling, the maximum stress of Nd:YAG overran 50% of the stress limit, thus increasing its tendency to fracture. Taken cooling time, fracture limit and obtainable size of the crystal into account, Nd:GGG should be the suitable active medium for high average power, repetitive frequency heat capacity laser.