A cooling system employs a single-acting positive displacement bellows pump to transfer a cryogenic liquid such as liquid nitrogen from a storage dewar to a heat exchanger coupled to a measurement chamber of an instrument, wherein cooling takes place by vaporizing the liquid. Preferably, the capacity of the pump is greater than the maximum cooling requirement of the instrument, wherein both vapor resulting from vaporizing of the cryogenic liquid circulated through the heat exchanger and liquid that does not vaporize when circulated through the heat exchanger are returned to the storage dewar, wherein the vapor is subsequently vented from the dewar. Preferably, with the aid of a weir in a return line, the level of liquid in the heat exchanger is maintained full and constant, and the cooling demands are automatically met without the need for other control of the flow rate or level of the liquid. Also, unlike conventional systems, liquid transfer from the dewar does not require dewar pressurization, so that the dewar may be refilled whenever necessary without interrupting the experiment in progress.