The optical axis of an infrared thermal imaging folding optical system is prone to shift owing to decentering of the tilt of optical components under complex environmental conditions, which affects the indication accuracy of the system for the target. Static sensitivity analysis of the optical axis for the optical system at the beginning of the design of the infrared thermal imaging system is useful for identifying the sensitive points of the optical system and provides constraints for the structural optimization design to meet the stability of the optical axis. The conversion relationship between the rotation process and spatial state quantities of the optical components was established by coordinate transformation based on the rotation matrix to simulate the spatial attitude of the optical component tilted in any direction and ensure that the Monte Carlo sampling in the optical axis sensitivity analysis corresponds to the constraint conditions of the structural design. On this basis, the flow of the static sensitivity analysis of the optical axis of the infrared folding optical system was established, and a program was compiled. A typical infrared thermal imaging folding optical system was analyzed using this program. According to the index requirements of the optical axis stability, the optical axis sensitivity and inverse sensitivity of the decenter and tilt of each optical component in the optical system were analyzed, and the initial tolerance limit was obtained. Then, Monte Carlo analysis sampling could be performed in any direction according to the initial tolerance limit data; thus, the decenter and tilt tolerance limit data that meet the optical axis stability index could be obtained, and the accuracy of the obtained data was verified by establishing a multi-coordinate system. Static sensitivity analysis provides a foundation for guiding the design of optical–mechanical thermal optimization.