The aerothermodynamic performance test is a prerequisite for investigating the turbine transition process. To enhance the safety and feasibility of the experiments while reducing energy costs, the target high-temperature transition processes must be converted to low-temperature ones based on the similarity criteria. However, the commonly used similarity criteria for turbine aerothermal performance are only applicable to steady states, rather than transition processes. This study presents a set of similarity criteria for turbines operating within non-periodic transition processes, according to the similarity of the dimensionless Navier-Stokes equations and time-variant definite conditions. Furthermore, the proposed similarity method ensures the similarity of the hysteresis effect by maintaining the uniformity of the dimensionless moments between the high- and low-temperature operating conditions. Comprehensive validations are carried out on two different turbines operating within transition processes, covering periodic processes with different pulsating frequencies and amplitudes, as well as non-periodic ones. Both the proposed and commonly used similarity methods are applied to obtain low-temperature performance curves, and the two curves are compared with the target high-temperature curve to evaluate the similarity accuracy of the corresponding methods. Regarding the deviations in the reduced power output between the high- and low-temperature operating conditions, the proposed similarity method exhibits similarity errors of no more than 2%, which is only approximately 20% of the errors produced by the commonly used method. Thus, the proposed similarity method has a high accuracy and is applicable to non-periodic transition processes.