1. A method of supplying a Joule-Thompson cooler comprising a high-pressure conduit (19) which terminates in an high-pressure orifice (21), and a low-pressure draining circuit (24-16-17) in a heat exchange relationship with the high-pressure conduit (19) and into which the expansion orifice (21) opens, this method being of the type in which the high-pressure conduit (19) is supplied successively with a priming fluid and then with a working fluid, characterised in that the change from the priming fluid to the working fluid occurs when the cooling rate provided by the first fluid falls below the cooling rate provided by the second fluid and in that the working fluid is initially used at a high rate of flow, after which its rate of flow is abruptly reduced to end the cooling stage of the cooler.
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