Abstract: A miniature open circuit refrigerator of the Joule-Thompson type, functions as a demand cryostat by virtue of a pressure-operated refrigerant supply control. The refrigerant fluid under high pressure is introduced at a first relatively rapid flow rate into the cryostat through a calibrated opening that is fully open during the initial or start-up period of the device, for rapid cool down. This calibrated opening is thereafter at least partially closed by a valve which is urged open by a spring and which is urged closed, against the action of the spring, by a bellows containing a gas at high pressure and which is exposed on its outer side to at least a portion of the pressure of the refrigerant fluid. Upon the fall in pressure of the stored refrigerant fluid, toward the end of the start-up, the bellows expands so as at least partially to close the valve, thereby to decrease the flow of refrigerant during the final portion of the cool-down period and during the steady state or on-stream operation of the device.