A superconducting magnet assembly includes a cryostat, a vacuum vessel and a refrigeration stage. An NMR probe using the assembly includes comprises cooled probe components, a two-stage cryocooler, and a counter flow heat exchanger. A cooling circuit guides coolant from one outlet of the counter flow heat exchanger back to an inlet of the counter flow heat exchanger via the second cooling stage, a cooled probe component, and a heat exchanger in the cryostat or a heat exchanger in a helium suspension tube. Both the intake temperature of the coolant flowing into the heat exchanger in the cryostat or in the suspension tube and the return flow temperature of the emerging coolant are at least 5 K lower than the operating temperature of the first cooling stage. Excess cooling capacity of the cryocooler reduces the evaporation rate of liquid helium or cools a superconducting magnet in a cryogen-free cryostat.