This study focuses on a thermodynamic performance analysis of a subcritical cascade refrigeration system (CRS) with internal heat exchangers (IHXs) using R41/R601, R41/R602A, and R41/cyclopentane as refrigerant pairs. The effect of evaporator temperature (Tev), condenser temperature (Tcond), and temperature difference in the cascade heat exchanger (ΔTCHX) on examined performance parameters are investigated. Each performance parameter is scrutinized by an optimum low-temperature circuit (LTC) condenser temperature. The operating parameters have some implications on the overall thermodynamic performance of the system. A change of 10 °C in the Tev and Tcond affects the performance of the system by approximately +26% and −8%, respectively. Moreover, a variation of 1 °C in the ΔTCHX reduces the performance of the system by about 2%. The effect of IHXs on the system has some interesting results. The coefficient of performance (COP) and exergy efficiency values of the system using R41/cyclopentane tend to constantly decrease by nearly 4.05%. Although not as much as R41/cyclopentane, there is also a slight drop in the performance of other refrigerant pairs. The discharge temperature in LTC and high-temperature circuit (HTC) compressors exceeds 120 °C for low-temperature refrigeration requirements, which is highly undesirable. Furthermore, the top priority components for the system improvement are HTC condenser, HTC compressor, and CHX. The refrigerant pairs with the thermodynamic performance from best to worst are R41/R601, R41/cyclopentane, and R41/R602A, respectively. Finally, the COP and exergy efficiency values of the modeled system are 10.40% higher and 3.06% lower, respectively, compared with current models in the literature.