Compared to other Joule-Thomson (J-T) refrigeration systems, open-cycle miniature J-T cryocoolers offer exceptional rapid cooling capabilities, making them ideal for applications such as infrared guidance in missiles. The energy recovery in the heat exchanger enables the refrigerant reach saturation temperature quickly and improve the jet liquefaction rate. The heat transfer intensity of the impinging jet determines the cooling rate of the target. Hence, heat recovery and the impact jet process are the primary factors behind this rapid cooling, with distinct roles that require separate consideration. The structural differences will directly affect the energy recovery and jet impact process. To investigate these affects, an experimental system for rapid cooling J-T cryocoolers was established and three distinct cryocoolers with substantial structural variations were designed. The important structures, including jet height, orifice diameter, enhanced heat transfer treatment of the cold plate, heat exchanger height, and heat exchanger cone angle, were closely studied. In the range of our experiments, it was found that larger heat exchanger cone angle leading better energy recovery performance, while the length of the heat exchanger is limited by the type of refrigerant. Longer heat exchanger actually introduce too much thermal mass for the refrigerant with better energy recovery performance. In the aspect of jet impingement, enhanced heat transfer treatment and larger jet height will improve the jet heat transfer intensity.