Abstract: The thermally coupled two-stage pulse tube cryocooler, characterized by its compact structural configuration and exceptional operational stability and reliability, demonstrates significant potential and promises application prospects in the field of space-borne cryogenic refrigeration within the liquid hydrogen temperature range. Therefore, comprehensive research on its performance characteristics and optimization approaches is of substantial importance. Based on theoretical analysis, this study established a numerical model of a thermally coupled two-stage pulse tube cryocooler using Sage software. By integrating the response surface optimization method, we systematically investigated the effects of precooling temperature and low-temperature stage input power on the cryocooler performance of the low-temperature stage. The results indicate that the refrigeration capacity of the low-temperature stage decreases with increasing precooling temperature but increases with higher input power to the low-temperature stage. Regarding the relative Carnot efficiency of the low-temperature stage, the precooling temperature exhibits a more pronounced influence compared to the input power to the low-temperature stage. Through response surface optimization analysis, it was determined that the relative Carnot efficiency of the low-temperature stage reaches its peak of 4.3% under operating conditions of 67.8 K precooling temperature and 248.6 W input power to the low-temperature stage, achieving a refrigeration capacity of 1.476 W at the refrigeration temperature of 20 K, with a minimum no-load temperature of 13.03 K. This study elucidates the influence mechanisms of precooling temperature and low-temperature stage input power on the cryocooler performance in a thermally coupled two-stage pulse tube cryocooler, providing valuable insights for parameter optimization and system design of this type of cryocooler.