The thermal management technique of multi-layer Cr4+:YAG medium was presented for mitigating the deleterious impact of thermal effects in a cryogenic helium gas cooled Yb:YAG multislab amplifier with Cr4+:YAG interlayers operating at a high repetition rate, by means of optimizing the architectures of Cr4+:YAG interlayers and claddings in the laser slabs. The distributions of temperature, stress, depolarization losses and optical path difference in four amplifier architectures with different Cr4+:YAG parameters were numerically calculated by a three-dimensional finite element analysis and the Jones matrices method. Based on these results of the propsed modelling, it was showed that the properly designed two-layer and three-layer Cr4+:YAG could decrease the heat deposition of the Cr4+:YAG around the gain media, and hence result in a very small transverse temperature gradient (<1.5 K) in the first slab. When the laser beam traveled through the whole amplifier, the average thermal-stress induced depolarization losses and optical path difference for the laser amplifier head were reduced to 0.5% and 0.8 ?姿, respectively. Furthermore, the negative impact of thermal effects on the output beam quality can be vanished by properly designing the number, widths, and absorption coefficients of the multi-layer Cr4+:YAG medium, which are beneficial for the engineering/design of the next generation of high energy, high power lasers.