The torque tubes of a superconducting generator belong to a unique class of heat exchangers where a single fluid stream (boil off helium vapour) exchanges heat with a metallic wall conducting heat from the ambient to the cold (liquid helium) space. The rate of heat leak to the cold space is the chief indicator of the performance of the exchanger. This rate of heat inleak has been found to be a function of two dimensionless parameters: a generalized cooling parameter A* and a temperature range parameter Ψ. A generalized design chart is presented which expresses the dimensionless heat flow rate Qc in terms of the parameters A* and Ψ. This chart will be useful for the design of torque tubes and vapour-cooled support members in cryogenic systems.