Single-pressure refractive-index gas thermometry (SPRIGT) is a new type primary thermometry jointly developed by TIPC of CAS in China and LNE-Cnam in France. To realize a competitive uncertainty of 0.25 mK for the thermodynamic temperature measurement, a cryogen-free cryostat with high-stability better than 0.2 mK should be designed. This paper presented the first experimental results of temperature control for this cryostat. To realize this objective, multi-layer radiation shields combined with a thermal-resistance method were used to isolate the thermal-noise from surroundings. Besides, a new temperature control method based on a gas-type heat switch and proportional-integral-derivative control method was proposed, which was applicable to different temperature ranges by changing the working modes of the heat switch. After optimizing, the ultra-high precision temperature control in the range of 5-25 K has been fully realized, which was the temperature instability (with standard deviation) of 0.021 mK at 5.0 K, 0.05 mK at 5.7 K, 0.042 mK at 7.4 K, 0.029 mK at 14.3 K, and 0.022 mK at 25 K with the sampling time of 0.8 s. This was almost the best reporting result in the world and showed its great potential in SPRIGT.