Passive Q-switched lasers are widely used in industrial manufacturing, medical treatment, defense and scientific research. However, systematic investigations into the thermal degradation mechanisms of Cr⁴⁺:YAG saturable absorbers under high-power pumping conditions remain insufficient. In this work, a side-pumped quasi-continuous-wave standing-wave laser oscillator is constructed to elucidate quantitatively the spatiotemporal coupling mechanism between thermally-induced refractive index gradients in Cr⁴⁺:YAG crystals and output beam distortion. Experimental results indicate that the direction and intensity of beam distortion are closely correlated with the thermal effect intensity distribution in Cr⁴⁺:YAG crystals, causing multi-peak modulation on the trailing edge of the temporal waveform and an increase in the number of resonant longitudinal modes. Moreover, increasing the initial transmittance of the Cr⁴⁺: YAG crystals effectively suppresses thermal effects, and using multiple high-transmittance crystals in series can further enhance the repetition rate capacity of passive Q-switched lasers. This research not only refines the thermal dynamic model of saturable absorbers but also establishes a novel thermal management paradigm for high-power passively Q-switched laser design, providing critical guidance for passively Q-switched technology in high-power and superior beam quality laser systems.