Low-temperature superconductivity and space exploration urgently require compact, highly reliable, and long-lifespan cooling technologies that operate at the liquid-helium temperature. Multistage Stirling-type pulse tube cryocoolers are a promising solution. In this study, a thermally coupled three-stage Stirling-type pulse tube cryocooler was designed and constructed. The system employs a two-stage high-frequency (70 Hz) Stirling cryocooler (model TC3130, Lihan) to precool the third stage, thus providing cooling capacities of 5 W and 2 W at 70 K and 32 K, respectively. For the third stage, simplified models were first established using Sage to determine the key operating parameters, including the operating frequency, average pressure, and precooling temperature. The third stage was fully simulated, followed by the final design and experimental set up. Experimental results show that under an average pressure of 1.4 MPa, a frequency of 21 Hz, and a total input power of approximately 370 W, the lowest no-load temperature reached 5.16 K, with typical cooling capacities of 50 mW and 102 mW at 6 K and 7 K, respectively.